School of Business Management

2022/23 Semester 1

BM3034 Business Statistics

ICA 3

Individual Assignment Guide

Date of Issue: Monday, 4 Jul 2022 (through NYP LMS)

Date of Submission: Monday, 15 Aug 2022, 2359 hours (through NYP LMS)

Individual Assignment Guide / BM3034 / Page 2

1.

Assignment Outline

This individual assignment constitutes 45% of the overall assessment for the

module, BM3034 Business Statistics. The assignment covers topics on

continuous probability distribution, sampling distribution of the sample means,

statistical estimation and hypothesis testing. You will solve problems in the above

topics and submit a report on how you apply the statistical concepts to facilitate

your decision-making process when conducting a business survey research.

Learners will submit on an individual basis, a typewritten report in MS Word with

supporting appendices on the raw data and statistical output in MS Excel.

2.

Learning Outcomes

After the completion of this assignment, learners will be able to:

•

•

•

3.

Solve problems using concepts on the continuous probability distribution.

Select a representative sample when conducting business survey research

by applying theories of the sampling distribution of the sample means.

Perform inferential statistics on real-life data using statistical estimation and

hypothesis testing techniques.

Requirements

Please approach your tutor if you have any query about the instructions indicated

below:

3.1 Continuous Probability Distribution (25 marks)

Each learner must use one (1) of the following three (3) continuous

probability distribution cases listed below based on the instructions given.

•

For learners whose admission number ends with the numbers

“0,1,2,3” solve Case 1.

•

For learners whose admission number ends with the numbers

“4,5,6” solve Case 2.

•

For learners whose admission number ends with the numbers

“7,8,9” solve Case 3.

Case 1

According to the traffic statistics by LTA, the speed of

vehicles that travel along PIE is normally distributed with a

mean of 88 km/h and a standard deviation of 21 km/h.

Case 2

Based on a health care researcher of a hospital, the height

of female individuals aged 15-25 is normally distributed with

a mean of 159 cm and a standard deviation of 16 cm.

Individual Assignment Guide / BM3034 / Page 3

Case 3

According to a sport & wellness professional, the weight of

male individuals aged 35-45 is normally distributed with a

mean of 72 kg and a standard deviation of 19 kg.

Based on your case assigned, solve the following problems using

continuous probability distribution techniques. Diagram is not needed in

your answer. Write down your answers with appropriate workings in your

report. State clearly the case that you are solving. Example: 3.1

Continuous Probability Distribution Case 1, 2 or 3.

(a)

State the variance and how the normal curve will change when the

mean decreases and the standard deviation increases.

(3 marks)

(b)

Determine with appropriate calculations if you agree or disagree with

the statement that “95.44% of the population items lies within 2

standard deviations of the population mean.”

(4 marks)

(c)

Calculate the amount for the top and bottom kth percentage of the

population, where k is your register number in your class register.

Show all the steps required.

(12 marks)

(d)

Calculate the probability that an individual in the population (X) is

more than 4 standard deviations bigger than the population mean.

Explain if it is possible to find such an individual in the population with

reference to your case scenario.

(6 marks)

3.2 Sampling Distribution of the Sample Means (25 marks)

A survey research is a tool used by businesses to obtain feedback from

their customers, suppliers or employees. One of the requirements to obtain

good feedback from their respondents when conducting a survey is to

select a representative sample for the survey.

For this assignment, you are the business personnel who is conducting a

survey for your company to obtain an estimate on the population mean.

Write a 750-word reflection on how the concepts and theorem(s) taught in

the topic “Sampling Distribution of the Sample Means” can facilitate your

decision-making process in conducting the business survey research, such

as choosing an appropriate sample size for the survey as well as other

considerations, costs and benefits.

Your reflection should provide discussion and explanation for the following

areas:

Individual Assignment Guide / BM3034 / Page 4

(a)

How do the concepts and theorem(s) in the topic “Sampling

Distribution of the Sample Means” influence your decision in choosing

an appropriate (or minimum) sample size for the survey? (10 marks)

(b)

Is a bigger sample better for the survey? Discuss the benefits of

having a bigger sample for the survey with reference to the standard

error. Any possible costs associated with a bigger sample selected?

How do you decide on the sample size for your survey?

(5 marks)

(c)

Besides the knowledge gained in the topic, suggest any three (3)

measures that you can undertake to obtain good feedback from your

respondents when conducting the survey. Be as innovative as

possible and provide reasons and elaborations to support your

suggestions.

(10 marks)

3.3 Statistical Estimation (25 marks)

Each learner must use one (1) of the following two (2) statistical estimation

cases listed below based on the instructions given.

•

For learners whose admission number ends with letters “A” to

“O”, solve Case 1.

•

For learners whose admission number ends with letters “P” to “Z”,

solve Case 2.

Case 1

Covid19 has highlighted the importance of strict hygiene and

more frequent cleaning and disinfection of hotel

accommodation. A hotel is keen to automate the disinfection

process and is evaluating a new cleaning and disinfection

robot for a month. Currently it takes the housekeeping staff

an average of 65 minutes to disinfect a room. The hotel

management aims to reduce the average disinfection time by

half. If the upper confidence limit of the interval estimate on

the population mean disinfection time by the robot does not

meet the target, the robot will not be purchased, vice versa.

A random sample of hotel rooms cleaned by the robot was

selected and the disinfection time was recorded during the

trial month. The data collected is shown in Appendix 1.

Individual Assignment Guide / BM3034 / Page 5

Case 2

A new Italian restaurant wanted to determine the price that it

should charge for its new signature dish, FB Risotto. The

restaurant intended to price the dish at more than $85 and

was concerned about the impact of price on the popularity of

the new dish. To determine the optimum price to charge, a

random sample of potential customers was surveyed on the

price they would be willing to pay for the dish. If the upper

confidence limit of the interval estimate on the population

mean price is above $85, the manager would price the dish

accordingly, vice versa. The data collected is shown in

Appendix 1.

The sample size taken for each learner is n=15+k, where k is your register

number in your class register. For example, if your class register number

is 1, the sample size that you will select is n=15+1=16. Thus, you will select

the first n=16 from the relevant sample data in Appendix 1 and perform the

appropriate calculations. Likewise, if your class register number is 20, the

sample size that you will select is n=15+20=35. Thus, you will select the

first n=35 from the relevant sample data in Appendix 1 and perform the

appropriate calculations.

Based on your case assigned, solve the following problems using statistical

estimation techniques. Diagram is not needed in your answer. Write down

your answers with appropriate workings in your report. State clearly the

case that you are solving. Example: 3.3 Statistical Estimation Case 1 or

2

(a)

Copy the sample data tabulated in appendix 1 and paste them into

MS Excel and perform descriptive statistics on the data using MS

Excel Data Analysis Tool Pak. Refer to the detailed illustration and

instructions on how to perform descriptive statistics from the video

lectures taught in class and in NYP LMS. Save the raw data and the

output of the descriptive statistics on the same worksheet and submit

them in the appendix section.

(2 marks)

(b)

State the point estimates for the population mean and standard

deviation.

(2 marks)

(c)

Calculate the 95% confidence interval for the population mean. Show

all the required calculations.

(9 marks)

(d)

Determine the decision for your case above.

(e)

Suggest how to improve the reliability and precision of the confidence

interval calculated. Calculate the minimum sample size which can

reduce the width of the confidence interval by half.

(9 marks)

(3 marks)

Individual Assignment Guide / BM3034 / Page 6

3.4 Hypothesis testing (25 marks)

Each learner must solve one (1) of the following two (2) hypothesis testing

cases listed below based on the instructions given.

•

For learners whose admission number ends with an odd number

(1,3,5,7,9), solve Case 1.

•

For learners whose admission number ends with an even number

(2,4,6,8,0), solve Case 2.

Case 1

According to a marketing personnel, the daily revenue target

of a new product set by management was $25,000 per day.

The marketing personnel convened a survey to measure the

daily revenue of the new product to determine if the average

actual revenue was below the target. If the average actual

revenue was below the target, more money will be spent on

marketing the new product. The data collected is shown in a

table in Appendix 1. Determine if the population mean daily

revenue of the product was below the target with a

hypothesis test at 1% level of significance. The data collected

is shown in Appendix 1

Case 2

A restaurant was evaluating if its customer service standard

needs to be enhanced. Management had determined that if

the average satisfaction score of its customers fell below 70

points, corrective actions would be undertaken. To measure

the satisfaction score of its customers, a survey was

commissioned. The data collected is shown in a table in

Appendix 1. Determine if the average satisfaction score of

its customers fell below 80 points with a hypothesis test at

5% significance level. The data collected is shown in

Appendix 1

The sample size taken for each learner is n=44-k, where k is your register

number in your class register. For example, if your class register number

is 1, the sample size that you will select is n=44-1=43. Thus, you will select

the first n=43 from the relevant sample data in Appendix 1 and perform the

appropriate calculations. Likewise, if your class register number is 20, the

sample size that you will select is n=44-20=24. Thus, you will select the

Individual Assignment Guide / BM3034 / Page 7

first n=24 from the relevant sample data in Appendix 1 and perform the

appropriate calculations.

Based on your case assigned, solve the following problems using

hypothesis testing methodology. Diagram is not needed in your answer.

Write down your answers with appropriate workings in your report. State

clearly the case that you are solving. Example: 3.4 Hypothesis Testing

Case 1 or 2.

4.

(a)

Copy the relevant sample data tabulated in appendix 1 and paste

them into MS Excel and perform descriptive statistics on the data

using MS Excel Data Analysis Tool Pak. Refer to the detailed

illustration and instructions on how to perform descriptive statistics

from the video lectures taught in class and in NYP LMS. Save the raw

data and the output of the descriptive statistics on the same worksheet

and submit them in the appendix section.

(2 marks)

(b)

State the values of the sample mean and sample standard deviation.

(2 marks)

(c)

Determine the conclusion for your case above using a hypothesis

test. Show all the calculations required.

(11 marks)

(d)

Describe type I and II errors.

(e)

Explain the consequences of committing type I and type II errors

respectively. Suggest how to adjust the significance level to minimise

type I and type II errors respectively.

(6 marks)

(4 marks)

Submissions

Report Format

• A written report of not more than 7 pages (excluding cover page and

appendices)

• Arial Font size 12 with single spacing must be submitted by each

individual learner.

• Please assign your file name for submission with the following format:

BM3034_Class_Name_Admin Number e.g.

BM3034_HA_Soh Eazi_1234567A

Your report should clearly label the following parts:

i)

Cover Page: Include a cover page with the assignment title (BM3034 ICA

3: Business Statistics Individual Assignment), name and admission

number of the learner.

Individual Assignment Guide / BM3034 / Page 8

ii)

Continuous Probability Distribution: Solutions for the case assigned to

you.

iii)

Sampling Distribution of the Sample Means: A reflection of not more

than 750 words (inclusive within the 7-page limit) on the topic that consists

of discussion and explanation for the areas required as mentioned above.

iv)

Statistical Estimation: Solutions for the case assigned to you.

v)

Hypothesis Testing: Solutions for the case assigned to you.

vi)

Appendix: providing the raw sample data of the statistical estimation and

hypothesis testing cases assigned and the output of the descriptive

statistics generated by the MS Excel Data Analysis Tool Pak.

Submission through Turnitin in NYP LMS and Due Date

The report is to be submitted through Turnitin latest by Monday,15 Aug

2022, 2359 hours. Turnitin is a cloud-based solution with capabilities in

originality checking using their OriginalityCheck tool. OriginalityCheck allows

your instructor to monitor assignment submissions and identify potential cases

of plagiarism by automatically comparing submissions to an online database of

original content. It is the responsibility of the learners to ensure that the matching

text highlighted in the Turnitin similarity report is properly referenced.

1.

Please read the following guide on how to submit your report in Politemall:

https://help.turnitin.com/feedback-studio/d2l/student/submitting-apaper/submitting-a-paper.htm

2.

Learners can also view the following video to learn how to submit your

report in Politemall:

Late submission and penalties

A penalty of 5% on the base marks to be deducted for each working day of late

submission from the respective assessment marks allocated should the report

be submitted late. Any late submission after 5 working days will be awarded zero

mark.

Plagiarism

Plagiarism is serious matter. Plagiarism is the act of taking and using the whole

or any part of ideas, words or works of other people and passing it off as one’s

Individual Assignment Guide / BM3034 / Page 9

own work, without acknowledgement of the original source. The act of

plagiarism is an offence under NYP Academic Integrity Policy:

https://www.nyp.edu.sg/current-students/academic-matters/nyp-academicintegrity.html. Any act of plagiarism may be construed as academic dishonesty.

A candidate who, after due disciplinary process, is found to have committed an

act that contravenes academic integrity in any assessment of a module would

be liable for disciplinary action under NYP Academic Integrity Policy.

It is also important not to share your or your team’s work with other learner(s) or

team(s). ALL parties involved in any act of plagiarism (including learner(s)

or team(s) who have shared their work with others) would be liable for

disciplinary action under NYP Academic Integrity Policy. If any learner had

asked you to share your work with him/her, it is important to turn down his/her

request and report the incident immediately to your module tutor to safeguard

your integrity.

All content from online or other primary sources should be properly referenced

(even if you are paraphrasing). Learners can use https://www.scribbr.com/apacitation-generator/ or other online citation generator to properly state the source

of the reference (websites, journal articles, books and reports) in the American

Psychological Association (APA) format. The APA format is a writing style and

format for academic documents such as scholarly journal articles and

books. When in doubt, the rule is to acknowledge the source.

A Turnitin Similarity Report generated provides detailed information about the

matches found between a learner’s submitted work and existing sources.

Learners can use the report to review their submissions for originality and identify

the specific areas of their submitted work where proper referencing are required.

Failing to do so may lead to plagiarism being reported in Turnitin.

5.

When an assignment is submitted using Turnitin, the Turnitin Similarity Report is

normally available within 15-30 minutes. However, a slight delay may occur

between the upload and the availability of the Similarity Report during periods of

high usage. Hence, learners are encouraged to submit their report at least one

day before the submission deadline so that they have sufficient time to make any

necessary amendment and resubmission before the submission deadline

expires.

Assessment

The assignment written report carries a total of 100 marks and constitutes 45%

of the overall grade for the module. The breakdown of marks is as follows:

The evaluation criteria for the written report is as follow:

Individual Assignment Guide / BM3034 / Page 10

Continuous Probability Distribution (25 marks)

i)

Correct solutions for the assigned case.

Sampling Distribution of the Sample Means (25 marks)

A coherent reflection of the topic that provides adequate discussion,

elaboration and explanation. The details of the rubrics are attached in

Appendix 2.

Statistical Estimation (25 marks)

i)

Correct solutions for the assigned case.

Hypothesis Testing (25 marks)

i)

Correct solutions for the assigned case.

Individual Assignment Guide / BM3034 / Page 11

Appendix 1

Sample data for statistical estimation and hypothesis testing questions.

Obtain the sample data from the MS Word document named “Appendix 1Sample data for statistical estimation and hypothesis testing questions” in the

NYP LMS.

Individual Assignment Guide / BM3034 / Page 12

Appendix 2-Scoring Rubric of Reflection

Evaluation Criteria

Concepts and

theorem(s) in the

topic and

appropriate

(minimum) sample

size chosen

(10 marks)

Exceed

Expectations

9-10 marks

Concepts and

theorem(s) are all

stated correctly.

Appropriate

(minimum) sample

size chosen is

correct.

Excellent

explanation and

elaboration

provided.

Benefits and costs

of a big sample size

(5 marks)

Meet

Expectations

7-8 marks

Approaching

Expectations

5-6 marks

Below

Expectations

3-4 marks

Inadequate

Concepts and

theorem(s) are

mostly stated

correctly.

Concepts and

theorem(s) are

stated with some

errors.

Concepts and

theorem(s) are

stated with a lot of

errors.

No concept or that

concepts and

theorem(s) are

stated wrongly.

Appropriate

(minimum) sample

size chosen is

correct.

Appropriate

(minimum) sample

size chosen is

correct.

Appropriate

(minimum) sample

size chosen is

wrong.

Appropriate

(minimum) sample

size chosen is

wrong.

Good explanation

and elaboration

provided.

Average

explanation and

elaboration

provided.

Poor explanation

and elaboration

provided.

No/ wrong

explanation and

elaboration

provided.

1-2 marks

5 marks

4 marks

3 marks

2 marks

1 mark

Excellent

explanation and

elaboration of the

benefits and costs

of having a big

sample size.

Good explanation

and elaboration of

the benefits and

costs of having a

big sample size.

Average

explanation and

elaboration of the

benefits and costs

of having a big

sample size.

Poor explanation

and elaboration of

the benefits and

costs of having a

big sample size.

No/ wrong

explanation and

elaboration of the

benefits and costs

of having a big

sample size.

Individual Assignment Guide / BM3034 / Page 13

Decision made on

the sample size to

take with excellent

explanation.

Suggestions on

three measures to

obtain good

feedback from

respondents

(10 marks)

Decision made on

the sample size to

take with average

explanation.

Decision made on

the sample size to

take with poor

explanation.

No decision made

on the sample size

to take.

9-10 marks

Decision made on

the sample size to

take with good

explanation.

7-8 marks

5-6 marks

3-4 marks

1-2 marks

All three

suggestions

provided are valid

and innovative.

Most of the

suggestions

provided are valid

and innovative.

Some of the

suggestions

provided are valid

and innovative.

Some of the

suggestions are

invalid.

No suggestion

provided or that

suggestions are

invalid.

Excellent

elaboration on all

three suggestions

provided.

Good elaboration

on the suggestions

provided.

Average

elaboration on the

suggestions

provided.

Poor elaboration

on the suggestions

provided.

No elaboration on

the suggestions

provided.

.

END

Appendix 1-Sample data for statistical estimation and hypothesis testing

questions

Observation

Number

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

Disinfection time

(minutes)

Price willing to

pay ($)

Daily revenue of

new product ($)

Customer satisfaction

score (points)

20

21

15

25

22

30

20

33

21

26

20

25

22

24

35

15

13

59

62

15

13

22

20

26

67

45

24

19

18

44

44

36

21

24

23

32

30

41

25

80

81

45

35

55

46

66

85

92

87

86

95

78

94

78

80

86

99

89

82

75

75

75

100

94

77

87

100

97

25

33

82

85

100

90

94

99

95

33

22843

22456

23147

24151

28027

27676

22778

24777

26910

20261

25221

20544

26378

22443

21002

15889

21889

20445

23530

22974

20826

28754

32336

26186

20355

12909

21880

15669

31795

20736

21282

26105

24115

25796

26019

26501

21094

23002

22089

73

64

55

70

85

67

72

45

64

65

45

71

69

71

69

56

68

67

65

79

80

33

81

75

47

45

89

70

87

76

73

45

61

65

81

79

33

61

72

Observation

Number

40

41

42

43

44

45

46

47

48

49

50

Disinfection time

(minutes)

Price willing to

pay ($)

Daily revenue of

new product ($)

Customer satisfaction

score (points)

50

22

23

34

11

68

30

45

72

57

54

85

83

82

122

98

33

33

45

25

90

75

29914

29448

25729

13782

22553

25375

29103

23643

22284

28719

29756

45

80

63

81

76

78

88

86

65

61

71

School of Business Management

2022/23 Semester 1

BM3034 Business Statistics

ICA 3

Individual Assignment Guide

Date of Issue: Monday, 4 Jul 2022 (through NYP LMS)

Date of Submission: Monday, 15 Aug 2022, 2359 hours (through NYP LMS)

Individual Assignment Guide / BM3034 / Page 2

1.

Assignment Outline

This individual assignment constitutes 45% of the overall assessment for the

module, BM3034 Business Statistics. The assignment covers topics on

continuous probability distribution, sampling distribution of the sample means,

statistical estimation and hypothesis testing. You will solve problems in the above

topics and submit a report on how you apply the statistical concepts to facilitate

your decision-making process when conducting a business survey research.

Learners will submit on an individual basis, a typewritten report in MS Word with

supporting appendices on the raw data and statistical output in MS Excel.

2.

Learning Outcomes

After the completion of this assignment, learners will be able to:

•

•

•

3.

Solve problems using concepts on the continuous probability distribution.

Select a representative sample when conducting business survey research

by applying theories of the sampling distribution of the sample means.

Perform inferential statistics on real-life data using statistical estimation and

hypothesis testing techniques.

Requirements

Please approach your tutor if you have any query about the instructions indicated

below:

3.1 Continuous Probability Distribution (25 marks)

Each learner must use one (1) of the following three (3) continuous

probability distribution cases listed below based on the instructions given.

•

For learners whose admission number ends with the numbers

“0,1,2,3” solve Case 1.

•

For learners whose admission number ends with the numbers

“4,5,6” solve Case 2.

•

For learners whose admission number ends with the numbers

“7,8,9” solve Case 3.

Case 1

According to the traffic statistics by LTA, the speed of

vehicles that travel along PIE is normally distributed with a

mean of 88 km/h and a standard deviation of 21 km/h.

Case 2

Based on a health care researcher of a hospital, the height

of female individuals aged 15-25 is normally distributed with

a mean of 159 cm and a standard deviation of 16 cm.

Individual Assignment Guide / BM3034 / Page 3

Case 3

According to a sport & wellness professional, the weight of

male individuals aged 35-45 is normally distributed with a

mean of 72 kg and a standard deviation of 19 kg.

Based on your case assigned, solve the following problems using

continuous probability distribution techniques. Diagram is not needed in

your answer. Write down your answers with appropriate workings in your

report. State clearly the case that you are solving. Example: 3.1

Continuous Probability Distribution Case 1, 2 or 3.

(a)

State the variance and how the normal curve will change when the

mean decreases and the standard deviation increases.

(3 marks)

(b)

Determine with appropriate calculations if you agree or disagree with

the statement that “95.44% of the population items lies within 2

standard deviations of the population mean.”

(4 marks)

(c)

Calculate the amount for the top and bottom kth percentage of the

population, where k is your register number in your class register.

Show all the steps required.

(12 marks)

(d)

Calculate the probability that an individual in the population (X) is

more than 4 standard deviations bigger than the population mean.

Explain if it is possible to find such an individual in the population with

reference to your case scenario.

(6 marks)

3.2 Sampling Distribution of the Sample Means (25 marks)

A survey research is a tool used by businesses to obtain feedback from

their customers, suppliers or employees. One of the requirements to obtain

good feedback from their respondents when conducting a survey is to

select a representative sample for the survey.

For this assignment, you are the business personnel who is conducting a

survey for your company to obtain an estimate on the population mean.

Write a 750-word reflection on how the concepts and theorem(s) taught in

the topic “Sampling Distribution of the Sample Means” can facilitate your

decision-making process in conducting the business survey research, such

as choosing an appropriate sample size for the survey as well as other

considerations, costs and benefits.

Your reflection should provide discussion and explanation for the following

areas:

Individual Assignment Guide / BM3034 / Page 4

(a)

How do the concepts and theorem(s) in the topic “Sampling

Distribution of the Sample Means” influence your decision in choosing

an appropriate (or minimum) sample size for the survey? (10 marks)

(b)

Is a bigger sample better for the survey? Discuss the benefits of

having a bigger sample for the survey with reference to the standard

error. Any possible costs associated with a bigger sample selected?

How do you decide on the sample size for your survey?

(5 marks)

(c)

Besides the knowledge gained in the topic, suggest any three (3)

measures that you can undertake to obtain good feedback from your

respondents when conducting the survey. Be as innovative as

possible and provide reasons and elaborations to support your

suggestions.

(10 marks)

3.3 Statistical Estimation (25 marks)

Each learner must use one (1) of the following two (2) statistical estimation

cases listed below based on the instructions given.

•

For learners whose admission number ends with letters “A” to

“O”, solve Case 1.

•

For learners whose admission number ends with letters “P” to “Z”,

solve Case 2.

Case 1

Covid19 has highlighted the importance of strict hygiene and

more frequent cleaning and disinfection of hotel

accommodation. A hotel is keen to automate the disinfection

process and is evaluating a new cleaning and disinfection

robot for a month. Currently it takes the housekeeping staff

an average of 65 minutes to disinfect a room. The hotel

management aims to reduce the average disinfection time by

half. If the upper confidence limit of the interval estimate on

the population mean disinfection time by the robot does not

meet the target, the robot will not be purchased, vice versa.

A random sample of hotel rooms cleaned by the robot was

selected and the disinfection time was recorded during the

trial month. The data collected is shown in Appendix 1.

Individual Assignment Guide / BM3034 / Page 5

Case 2

A new Italian restaurant wanted to determine the price that it

should charge for its new signature dish, FB Risotto. The

restaurant intended to price the dish at more than $85 and

was concerned about the impact of price on the popularity of

the new dish. To determine the optimum price to charge, a

random sample of potential customers was surveyed on the

price they would be willing to pay for the dish. If the upper

confidence limit of the interval estimate on the population

mean price is above $85, the manager would price the dish

accordingly, vice versa. The data collected is shown in

Appendix 1.

The sample size taken for each learner is n=15+k, where k is your register

number in your class register. For example, if your class register number

is 1, the sample size that you will select is n=15+1=16. Thus, you will select

the first n=16 from the relevant sample data in Appendix 1 and perform the

appropriate calculations. Likewise, if your class register number is 20, the

sample size that you will select is n=15+20=35. Thus, you will select the

first n=35 from the relevant sample data in Appendix 1 and perform the

appropriate calculations.

Based on your case assigned, solve the following problems using statistical

estimation techniques. Diagram is not needed in your answer. Write down

your answers with appropriate workings in your report. State clearly the

case that you are solving. Example: 3.3 Statistical Estimation Case 1 or

2

(a)

Copy the sample data tabulated in appendix 1 and paste them into

MS Excel and perform descriptive statistics on the data using MS

Excel Data Analysis Tool Pak. Refer to the detailed illustration and

instructions on how to perform descriptive statistics from the video

lectures taught in class and in NYP LMS. Save the raw data and the

output of the descriptive statistics on the same worksheet and submit

them in the appendix section.

(2 marks)

(b)

State the point estimates for the population mean and standard

deviation.

(2 marks)

(c)

Calculate the 95% confidence interval for the population mean. Show

all the required calculations.

(9 marks)

(d)

Determine the decision for your case above.

(e)

Suggest how to improve the reliability and precision of the confidence

interval calculated. Calculate the minimum sample size which can

reduce the width of the confidence interval by half.

(9 marks)

(3 marks)

Individual Assignment Guide / BM3034 / Page 6

3.4 Hypothesis testing (25 marks)

Each learner must solve one (1) of the following two (2) hypothesis testing

cases listed below based on the instructions given.

•

For learners whose admission number ends with an odd number

(1,3,5,7,9), solve Case 1.

•

For learners whose admission number ends with an even number

(2,4,6,8,0), solve Case 2.

Case 1

According to a marketing personnel, the daily revenue target

of a new product set by management was $25,000 per day.

The marketing personnel convened a survey to measure the

daily revenue of the new product to determine if the average

actual revenue was below the target. If the average actual

revenue was below the target, more money will be spent on

marketing the new product. The data collected is shown in a

table in Appendix 1. Determine if the population mean daily

revenue of the product was below the target with a

hypothesis test at 1% level of significance. The data collected

is shown in Appendix 1

Case 2

A restaurant was evaluating if its customer service standard

needs to be enhanced. Management had determined that if

the average satisfaction score of its customers fell below 70

80 points, corrective actions would be undertaken. To

measure the satisfaction score of its customers, a survey

was commissioned. The data collected is shown in a table in

Appendix 1. Determine if the average satisfaction score of

its customers fell below 80 points with a hypothesis test at

5% significance level. The data collected is shown in

Appendix 1

The sample size taken for each learner is n=44-k, where k is your register

number in your class register. For example, if your class register number

is 1, the sample size that you will select is n=44-1=43. Thus, you will select

the first n=43 from the relevant sample data in Appendix 1 and perform the

appropriate calculations. Likewise, if your class register number is 20, the

sample size that you will select is n=44-20=24. Thus, you will select the

Individual Assignment Guide / BM3034 / Page 7

first n=24 from the relevant sample data in Appendix 1 and perform the

appropriate calculations.

Based on your case assigned, solve the following problems using

hypothesis testing methodology. Diagram is not needed in your answer.

Write down your answers with appropriate workings in your report. State

clearly the case that you are solving. Example: 3.4 Hypothesis Testing

Case 1 or 2.

4.

(a)

Copy the relevant sample data tabulated in appendix 1 and paste

them into MS Excel and perform descriptive statistics on the data

using MS Excel Data Analysis Tool Pak. Refer to the detailed

illustration and instructions on how to perform descriptive statistics

from the video lectures taught in class and in NYP LMS. Save the raw

data and the output of the descriptive statistics on the same worksheet

and submit them in the appendix section.

(2 marks)

(b)

State the values of the sample mean and sample standard deviation.

(2 marks)

(c)

Determine the conclusion for your case above using a hypothesis

test. Show all the calculations required.

(11 marks)

(d)

Describe type I and II errors.

(e)

Explain the consequences of committing type I and type II errors

respectively. Suggest how to adjust the significance level to minimise

type I and type II errors respectively.

(6 marks)

(4 marks)

Submissions

Report Format

• A written report of not more than 7 pages (excluding cover page and

appendices)

• Arial Font size 12 with single spacing must be submitted by each

individual learner.

• Please assign your file name for submission with the following format:

BM3034_Class_Name_Admin Number e.g.

BM3034_HA_Soh Eazi_1234567A

Your report should clearly label the following parts:

i)

Cover Page: Include a cover page with the assignment title (BM3034 ICA

3: Business Statistics Individual Assignment), name and admission

number of the learner.

Individual Assignment Guide / BM3034 / Page 8

ii)

Continuous Probability Distribution: Solutions for the case assigned to

you.

iii)

Sampling Distribution of the Sample Means: A reflection of not more

than 750 words (inclusive within the 7-page limit) on the topic that consists

of discussion and explanation for the areas required as mentioned above.

iv)

Statistical Estimation: Solutions for the case assigned to you.

v)

Hypothesis Testing: Solutions for the case assigned to you.

vi)

Appendix: providing the raw sample data of the statistical estimation and

hypothesis testing cases assigned and the output of the descriptive

statistics generated by the MS Excel Data Analysis Tool Pak.

Submission through Turnitin in NYP LMS and Due Date

The report is to be submitted through Turnitin latest by Monday,15 Aug

2022, 2359 hours. Turnitin is a cloud-based solution with capabilities in

originality checking using their OriginalityCheck tool. OriginalityCheck allows

your instructor to monitor assignment submissions and identify potential cases

of plagiarism by automatically comparing submissions to an online database of

original content. It is the responsibility of the learners to ensure that the matching

text highlighted in the Turnitin similarity report is properly referenced.

1.

Please read the following guide on how to submit your report in Politemall:

https://help.turnitin.com/feedback-studio/d2l/student/submitting-apaper/submitting-a-paper.htm

2.

Learners can also view the following video to learn how to submit your

report in Politemall:

Late submission and penalties

A penalty of 5% on the base marks to be deducted for each working day of late

submission from the respective assessment marks allocated should the report

be submitted late. Any late submission after 5 working days will be awarded zero

mark.

Plagiarism

Plagiarism is serious matter. Plagiarism is the act of taking and using the whole

or any part of ideas, words or works of other people and passing it off as one’s

Individual Assignment Guide / BM3034 / Page 9

own work, without acknowledgement of the original source. The act of

plagiarism is an offence under NYP Academic Integrity Policy:

https://www.nyp.edu.sg/current-students/academic-matters/nyp-academicintegrity.html. Any act of plagiarism may be construed as academic dishonesty.

A candidate who, after due disciplinary process, is found to have committed an

act that contravenes academic integrity in any assessment of a module would

be liable for disciplinary action under NYP Academic Integrity Policy.

It is also important not to share your or your team’s work with other learner(s) or

team(s). ALL parties involved in any act of plagiarism (including learner(s)

or team(s) who have shared their work with others) would be liable for

disciplinary action under NYP Academic Integrity Policy. If any learner had

asked you to share your work with him/her, it is important to turn down his/her

request and report the incident immediately to your module tutor to safeguard

your integrity.

All content from online or other primary sources should be properly referenced

(even if you are paraphrasing). Learners can use https://www.scribbr.com/apacitation-generator/ or other online citation generator to properly state the source

of the reference (websites, journal articles, books and reports) in the American

Psychological Association (APA) format. The APA format is a writing style and

format for academic documents such as scholarly journal articles and

books. When in doubt, the rule is to acknowledge the source.

A Turnitin Similarity Report generated provides detailed information about the

matches found between a learner’s submitted work and existing sources.

Learners can use the report to review their submissions for originality and identify

the specific areas of their submitted work where proper referencing are required.

Failing to do so may lead to plagiarism being reported in Turnitin.

5.

When an assignment is submitted using Turnitin, the Turnitin Similarity Report is

normally available within 15-30 minutes. However, a slight delay may occur

between the upload and the availability of the Similarity Report during periods of

high usage. Hence, learners are encouraged to submit their report at least one

day before the submission deadline so that they have sufficient time to make any

necessary amendment and resubmission before the submission deadline

expires.

Assessment

The assignment written report carries a total of 100 marks and constitutes 45%

of the overall grade for the module. The breakdown of marks is as follows:

The evaluation criteria for the written report is as follow:

Individual Assignment Guide / BM3034 / Page 10

Continuous Probability Distribution (25 marks)

i)

Correct solutions for the assigned case.

Sampling Distribution of the Sample Means (25 marks)

A coherent reflection of the topic that provides adequate discussion,

elaboration and explanation. The details of the rubrics are attached in

Appendix 2.

Statistical Estimation (25 marks)

i)

Correct solutions for the assigned case.

Hypothesis Testing (25 marks)

i)

Correct solutions for the assigned case.

Individual Assignment Guide / BM3034 / Page 11

Appendix 1

Sample data for statistical estimation and hypothesis testing questions.

Obtain the sample data from the MS Word document named “Appendix 1Sample data for statistical estimation and hypothesis testing questions” in the

NYP LMS.

Individual Assignment Guide / BM3034 / Page 12

Appendix 2-Scoring Rubric of Reflection

Evaluation Criteria

Concepts and

theorem(s) in the

topic and

appropriate

(minimum) sample

size chosen

(10 marks)

Exceed

Expectations

9-10 marks

Concepts and

theorem(s) are all

stated correctly.

Appropriate

(minimum) sample

size chosen is

correct.

Excellent

explanation and

elaboration

provided.

Benefits and costs

of a big sample size

(5 marks)

Meet

Expectations

7-8 marks

Approaching

Expectations

5-6 marks

Below

Expectations

3-4 marks

Inadequate

Concepts and

theorem(s) are

mostly stated

correctly.

Concepts and

theorem(s) are

stated with some

errors.

Concepts and

theorem(s) are

stated with a lot of

errors.

No concept or that

concepts and

theorem(s) are

stated wrongly.

Appropriate

(minimum) sample

size chosen is

correct.

Appropriate

(minimum) sample

size chosen is

correct.

Appropriate

(minimum) sample

size chosen is

wrong.

Appropriate

(minimum) sample

size chosen is

wrong.

Good explanation

and elaboration

provided.

Average

explanation and

elaboration

provided.

Poor explanation

and elaboration

provided.

No/ wrong

explanation and

elaboration

provided.

1-2 marks

5 marks

4 marks

3 marks

2 marks

1 mark

Excellent

explanation and

elaboration of the

benefits and costs

of having a big

sample size.

Good explanation

and elaboration of

the benefits and

costs of having a

big sample size.

Average

explanation and

elaboration of the

benefits and costs

of having a big

sample size.

Poor explanation

and elaboration of

the benefits and

costs of having a

big sample size.

No/ wrong

explanation and

elaboration of the

benefits and costs

of having a big

sample size.

Individual Assignment Guide / BM3034 / Page 13

Decision made on

the sample size to

take with excellent

explanation.

Suggestions on

three measures to

obtain good

feedback from

respondents

Decision made on

the sample size to

take with average

explanation.

Decision made on

the sample size to

take with poor

explanation.

No decision made

on the sample size

to take.

9-10 marks

Decision made on

the sample size to

take with good

explanation.

7-8 marks

5-6 marks

3-4 marks

1-2 marks

All three

suggestions

provided are valid

and innovative.

Most of the

suggestions

provided are valid

and innovative.

Some of the

suggestions

provided are valid

and innovative.

Some of the

suggestions are

invalid.

No suggestion

provided or that

suggestions are

invalid.

Excellent

elaboration on all

three suggestions

provided.

Good elaboration

on the suggestions

provided.

Average

elaboration on the

suggestions

provided.

Poor elaboration

on the suggestions

provided.

No elaboration on

the suggestions

provided.

.

(10 marks)

END

Purchase answer to see full

attachment

2022/23 Semester 1

BM3034 Business Statistics

ICA 3

Individual Assignment Guide

Date of Issue: Monday, 4 Jul 2022 (through NYP LMS)

Date of Submission: Monday, 15 Aug 2022, 2359 hours (through NYP LMS)

Individual Assignment Guide / BM3034 / Page 2

1.

Assignment Outline

This individual assignment constitutes 45% of the overall assessment for the

module, BM3034 Business Statistics. The assignment covers topics on

continuous probability distribution, sampling distribution of the sample means,

statistical estimation and hypothesis testing. You will solve problems in the above

topics and submit a report on how you apply the statistical concepts to facilitate

your decision-making process when conducting a business survey research.

Learners will submit on an individual basis, a typewritten report in MS Word with

supporting appendices on the raw data and statistical output in MS Excel.

2.

Learning Outcomes

After the completion of this assignment, learners will be able to:

•

•

•

3.

Solve problems using concepts on the continuous probability distribution.

Select a representative sample when conducting business survey research

by applying theories of the sampling distribution of the sample means.

Perform inferential statistics on real-life data using statistical estimation and

hypothesis testing techniques.

Requirements

Please approach your tutor if you have any query about the instructions indicated

below:

3.1 Continuous Probability Distribution (25 marks)

Each learner must use one (1) of the following three (3) continuous

probability distribution cases listed below based on the instructions given.

•

For learners whose admission number ends with the numbers

“0,1,2,3” solve Case 1.

•

For learners whose admission number ends with the numbers

“4,5,6” solve Case 2.

•

For learners whose admission number ends with the numbers

“7,8,9” solve Case 3.

Case 1

According to the traffic statistics by LTA, the speed of

vehicles that travel along PIE is normally distributed with a

mean of 88 km/h and a standard deviation of 21 km/h.

Case 2

Based on a health care researcher of a hospital, the height

of female individuals aged 15-25 is normally distributed with

a mean of 159 cm and a standard deviation of 16 cm.

Individual Assignment Guide / BM3034 / Page 3

Case 3

According to a sport & wellness professional, the weight of

male individuals aged 35-45 is normally distributed with a

mean of 72 kg and a standard deviation of 19 kg.

Based on your case assigned, solve the following problems using

continuous probability distribution techniques. Diagram is not needed in

your answer. Write down your answers with appropriate workings in your

report. State clearly the case that you are solving. Example: 3.1

Continuous Probability Distribution Case 1, 2 or 3.

(a)

State the variance and how the normal curve will change when the

mean decreases and the standard deviation increases.

(3 marks)

(b)

Determine with appropriate calculations if you agree or disagree with

the statement that “95.44% of the population items lies within 2

standard deviations of the population mean.”

(4 marks)

(c)

Calculate the amount for the top and bottom kth percentage of the

population, where k is your register number in your class register.

Show all the steps required.

(12 marks)

(d)

Calculate the probability that an individual in the population (X) is

more than 4 standard deviations bigger than the population mean.

Explain if it is possible to find such an individual in the population with

reference to your case scenario.

(6 marks)

3.2 Sampling Distribution of the Sample Means (25 marks)

A survey research is a tool used by businesses to obtain feedback from

their customers, suppliers or employees. One of the requirements to obtain

good feedback from their respondents when conducting a survey is to

select a representative sample for the survey.

For this assignment, you are the business personnel who is conducting a

survey for your company to obtain an estimate on the population mean.

Write a 750-word reflection on how the concepts and theorem(s) taught in

the topic “Sampling Distribution of the Sample Means” can facilitate your

decision-making process in conducting the business survey research, such

as choosing an appropriate sample size for the survey as well as other

considerations, costs and benefits.

Your reflection should provide discussion and explanation for the following

areas:

Individual Assignment Guide / BM3034 / Page 4

(a)

How do the concepts and theorem(s) in the topic “Sampling

Distribution of the Sample Means” influence your decision in choosing

an appropriate (or minimum) sample size for the survey? (10 marks)

(b)

Is a bigger sample better for the survey? Discuss the benefits of

having a bigger sample for the survey with reference to the standard

error. Any possible costs associated with a bigger sample selected?

How do you decide on the sample size for your survey?

(5 marks)

(c)

Besides the knowledge gained in the topic, suggest any three (3)

measures that you can undertake to obtain good feedback from your

respondents when conducting the survey. Be as innovative as

possible and provide reasons and elaborations to support your

suggestions.

(10 marks)

3.3 Statistical Estimation (25 marks)

Each learner must use one (1) of the following two (2) statistical estimation

cases listed below based on the instructions given.

•

For learners whose admission number ends with letters “A” to

“O”, solve Case 1.

•

For learners whose admission number ends with letters “P” to “Z”,

solve Case 2.

Case 1

Covid19 has highlighted the importance of strict hygiene and

more frequent cleaning and disinfection of hotel

accommodation. A hotel is keen to automate the disinfection

process and is evaluating a new cleaning and disinfection

robot for a month. Currently it takes the housekeeping staff

an average of 65 minutes to disinfect a room. The hotel

management aims to reduce the average disinfection time by

half. If the upper confidence limit of the interval estimate on

the population mean disinfection time by the robot does not

meet the target, the robot will not be purchased, vice versa.

A random sample of hotel rooms cleaned by the robot was

selected and the disinfection time was recorded during the

trial month. The data collected is shown in Appendix 1.

Individual Assignment Guide / BM3034 / Page 5

Case 2

A new Italian restaurant wanted to determine the price that it

should charge for its new signature dish, FB Risotto. The

restaurant intended to price the dish at more than $85 and

was concerned about the impact of price on the popularity of

the new dish. To determine the optimum price to charge, a

random sample of potential customers was surveyed on the

price they would be willing to pay for the dish. If the upper

confidence limit of the interval estimate on the population

mean price is above $85, the manager would price the dish

accordingly, vice versa. The data collected is shown in

Appendix 1.

The sample size taken for each learner is n=15+k, where k is your register

number in your class register. For example, if your class register number

is 1, the sample size that you will select is n=15+1=16. Thus, you will select

the first n=16 from the relevant sample data in Appendix 1 and perform the

appropriate calculations. Likewise, if your class register number is 20, the

sample size that you will select is n=15+20=35. Thus, you will select the

first n=35 from the relevant sample data in Appendix 1 and perform the

appropriate calculations.

Based on your case assigned, solve the following problems using statistical

estimation techniques. Diagram is not needed in your answer. Write down

your answers with appropriate workings in your report. State clearly the

case that you are solving. Example: 3.3 Statistical Estimation Case 1 or

2

(a)

Copy the sample data tabulated in appendix 1 and paste them into

MS Excel and perform descriptive statistics on the data using MS

Excel Data Analysis Tool Pak. Refer to the detailed illustration and

instructions on how to perform descriptive statistics from the video

lectures taught in class and in NYP LMS. Save the raw data and the

output of the descriptive statistics on the same worksheet and submit

them in the appendix section.

(2 marks)

(b)

State the point estimates for the population mean and standard

deviation.

(2 marks)

(c)

Calculate the 95% confidence interval for the population mean. Show

all the required calculations.

(9 marks)

(d)

Determine the decision for your case above.

(e)

Suggest how to improve the reliability and precision of the confidence

interval calculated. Calculate the minimum sample size which can

reduce the width of the confidence interval by half.

(9 marks)

(3 marks)

Individual Assignment Guide / BM3034 / Page 6

3.4 Hypothesis testing (25 marks)

Each learner must solve one (1) of the following two (2) hypothesis testing

cases listed below based on the instructions given.

•

For learners whose admission number ends with an odd number

(1,3,5,7,9), solve Case 1.

•

For learners whose admission number ends with an even number

(2,4,6,8,0), solve Case 2.

Case 1

According to a marketing personnel, the daily revenue target

of a new product set by management was $25,000 per day.

The marketing personnel convened a survey to measure the

daily revenue of the new product to determine if the average

actual revenue was below the target. If the average actual

revenue was below the target, more money will be spent on

marketing the new product. The data collected is shown in a

table in Appendix 1. Determine if the population mean daily

revenue of the product was below the target with a

hypothesis test at 1% level of significance. The data collected

is shown in Appendix 1

Case 2

A restaurant was evaluating if its customer service standard

needs to be enhanced. Management had determined that if

the average satisfaction score of its customers fell below 70

points, corrective actions would be undertaken. To measure

the satisfaction score of its customers, a survey was

commissioned. The data collected is shown in a table in

Appendix 1. Determine if the average satisfaction score of

its customers fell below 80 points with a hypothesis test at

5% significance level. The data collected is shown in

Appendix 1

The sample size taken for each learner is n=44-k, where k is your register

number in your class register. For example, if your class register number

is 1, the sample size that you will select is n=44-1=43. Thus, you will select

the first n=43 from the relevant sample data in Appendix 1 and perform the

appropriate calculations. Likewise, if your class register number is 20, the

sample size that you will select is n=44-20=24. Thus, you will select the

Individual Assignment Guide / BM3034 / Page 7

first n=24 from the relevant sample data in Appendix 1 and perform the

appropriate calculations.

Based on your case assigned, solve the following problems using

hypothesis testing methodology. Diagram is not needed in your answer.

Write down your answers with appropriate workings in your report. State

clearly the case that you are solving. Example: 3.4 Hypothesis Testing

Case 1 or 2.

4.

(a)

Copy the relevant sample data tabulated in appendix 1 and paste

them into MS Excel and perform descriptive statistics on the data

using MS Excel Data Analysis Tool Pak. Refer to the detailed

illustration and instructions on how to perform descriptive statistics

from the video lectures taught in class and in NYP LMS. Save the raw

data and the output of the descriptive statistics on the same worksheet

and submit them in the appendix section.

(2 marks)

(b)

State the values of the sample mean and sample standard deviation.

(2 marks)

(c)

Determine the conclusion for your case above using a hypothesis

test. Show all the calculations required.

(11 marks)

(d)

Describe type I and II errors.

(e)

Explain the consequences of committing type I and type II errors

respectively. Suggest how to adjust the significance level to minimise

type I and type II errors respectively.

(6 marks)

(4 marks)

Submissions

Report Format

• A written report of not more than 7 pages (excluding cover page and

appendices)

• Arial Font size 12 with single spacing must be submitted by each

individual learner.

• Please assign your file name for submission with the following format:

BM3034_Class_Name_Admin Number e.g.

BM3034_HA_Soh Eazi_1234567A

Your report should clearly label the following parts:

i)

Cover Page: Include a cover page with the assignment title (BM3034 ICA

3: Business Statistics Individual Assignment), name and admission

number of the learner.

Individual Assignment Guide / BM3034 / Page 8

ii)

Continuous Probability Distribution: Solutions for the case assigned to

you.

iii)

Sampling Distribution of the Sample Means: A reflection of not more

than 750 words (inclusive within the 7-page limit) on the topic that consists

of discussion and explanation for the areas required as mentioned above.

iv)

Statistical Estimation: Solutions for the case assigned to you.

v)

Hypothesis Testing: Solutions for the case assigned to you.

vi)

Appendix: providing the raw sample data of the statistical estimation and

hypothesis testing cases assigned and the output of the descriptive

statistics generated by the MS Excel Data Analysis Tool Pak.

Submission through Turnitin in NYP LMS and Due Date

The report is to be submitted through Turnitin latest by Monday,15 Aug

2022, 2359 hours. Turnitin is a cloud-based solution with capabilities in

originality checking using their OriginalityCheck tool. OriginalityCheck allows

your instructor to monitor assignment submissions and identify potential cases

of plagiarism by automatically comparing submissions to an online database of

original content. It is the responsibility of the learners to ensure that the matching

text highlighted in the Turnitin similarity report is properly referenced.

1.

Please read the following guide on how to submit your report in Politemall:

https://help.turnitin.com/feedback-studio/d2l/student/submitting-apaper/submitting-a-paper.htm

2.

Learners can also view the following video to learn how to submit your

report in Politemall:

Late submission and penalties

A penalty of 5% on the base marks to be deducted for each working day of late

submission from the respective assessment marks allocated should the report

be submitted late. Any late submission after 5 working days will be awarded zero

mark.

Plagiarism

Plagiarism is serious matter. Plagiarism is the act of taking and using the whole

or any part of ideas, words or works of other people and passing it off as one’s

Individual Assignment Guide / BM3034 / Page 9

own work, without acknowledgement of the original source. The act of

plagiarism is an offence under NYP Academic Integrity Policy:

https://www.nyp.edu.sg/current-students/academic-matters/nyp-academicintegrity.html. Any act of plagiarism may be construed as academic dishonesty.

A candidate who, after due disciplinary process, is found to have committed an

act that contravenes academic integrity in any assessment of a module would

be liable for disciplinary action under NYP Academic Integrity Policy.

It is also important not to share your or your team’s work with other learner(s) or

team(s). ALL parties involved in any act of plagiarism (including learner(s)

or team(s) who have shared their work with others) would be liable for

disciplinary action under NYP Academic Integrity Policy. If any learner had

asked you to share your work with him/her, it is important to turn down his/her

request and report the incident immediately to your module tutor to safeguard

your integrity.

All content from online or other primary sources should be properly referenced

(even if you are paraphrasing). Learners can use https://www.scribbr.com/apacitation-generator/ or other online citation generator to properly state the source

of the reference (websites, journal articles, books and reports) in the American

Psychological Association (APA) format. The APA format is a writing style and

format for academic documents such as scholarly journal articles and

books. When in doubt, the rule is to acknowledge the source.

A Turnitin Similarity Report generated provides detailed information about the

matches found between a learner’s submitted work and existing sources.

Learners can use the report to review their submissions for originality and identify

the specific areas of their submitted work where proper referencing are required.

Failing to do so may lead to plagiarism being reported in Turnitin.

5.

When an assignment is submitted using Turnitin, the Turnitin Similarity Report is

normally available within 15-30 minutes. However, a slight delay may occur

between the upload and the availability of the Similarity Report during periods of

high usage. Hence, learners are encouraged to submit their report at least one

day before the submission deadline so that they have sufficient time to make any

necessary amendment and resubmission before the submission deadline

expires.

Assessment

The assignment written report carries a total of 100 marks and constitutes 45%

of the overall grade for the module. The breakdown of marks is as follows:

The evaluation criteria for the written report is as follow:

Individual Assignment Guide / BM3034 / Page 10

Continuous Probability Distribution (25 marks)

i)

Correct solutions for the assigned case.

Sampling Distribution of the Sample Means (25 marks)

A coherent reflection of the topic that provides adequate discussion,

elaboration and explanation. The details of the rubrics are attached in

Appendix 2.

Statistical Estimation (25 marks)

i)

Correct solutions for the assigned case.

Hypothesis Testing (25 marks)

i)

Correct solutions for the assigned case.

Individual Assignment Guide / BM3034 / Page 11

Appendix 1

Sample data for statistical estimation and hypothesis testing questions.

Obtain the sample data from the MS Word document named “Appendix 1Sample data for statistical estimation and hypothesis testing questions” in the

NYP LMS.

Individual Assignment Guide / BM3034 / Page 12

Appendix 2-Scoring Rubric of Reflection

Evaluation Criteria

Concepts and

theorem(s) in the

topic and

appropriate

(minimum) sample

size chosen

(10 marks)

Exceed

Expectations

9-10 marks

Concepts and

theorem(s) are all

stated correctly.

Appropriate

(minimum) sample

size chosen is

correct.

Excellent

explanation and

elaboration

provided.

Benefits and costs

of a big sample size

(5 marks)

Meet

Expectations

7-8 marks

Approaching

Expectations

5-6 marks

Below

Expectations

3-4 marks

Inadequate

Concepts and

theorem(s) are

mostly stated

correctly.

Concepts and

theorem(s) are

stated with some

errors.

Concepts and

theorem(s) are

stated with a lot of

errors.

No concept or that

concepts and

theorem(s) are

stated wrongly.

Appropriate

(minimum) sample

size chosen is

correct.

Appropriate

(minimum) sample

size chosen is

correct.

Appropriate

(minimum) sample

size chosen is

wrong.

Appropriate

(minimum) sample

size chosen is

wrong.

Good explanation

and elaboration

provided.

Average

explanation and

elaboration

provided.

Poor explanation

and elaboration

provided.

No/ wrong

explanation and

elaboration

provided.

1-2 marks

5 marks

4 marks

3 marks

2 marks

1 mark

Excellent

explanation and

elaboration of the

benefits and costs

of having a big

sample size.

Good explanation

and elaboration of

the benefits and

costs of having a

big sample size.

Average

explanation and

elaboration of the

benefits and costs

of having a big

sample size.

Poor explanation

and elaboration of

the benefits and

costs of having a

big sample size.

No/ wrong

explanation and

elaboration of the

benefits and costs

of having a big

sample size.

Individual Assignment Guide / BM3034 / Page 13

Decision made on

the sample size to

take with excellent

explanation.

Suggestions on

three measures to

obtain good

feedback from

respondents

(10 marks)

Decision made on

the sample size to

take with average

explanation.

Decision made on

the sample size to

take with poor

explanation.

No decision made

on the sample size

to take.

9-10 marks

Decision made on

the sample size to

take with good

explanation.

7-8 marks

5-6 marks

3-4 marks

1-2 marks

All three

suggestions

provided are valid

and innovative.

Most of the

suggestions

provided are valid

and innovative.

Some of the

suggestions

provided are valid

and innovative.

Some of the

suggestions are

invalid.

No suggestion

provided or that

suggestions are

invalid.

Excellent

elaboration on all

three suggestions

provided.

Good elaboration

on the suggestions

provided.

Average

elaboration on the

suggestions

provided.

Poor elaboration

on the suggestions

provided.

No elaboration on

the suggestions

provided.

.

END

Appendix 1-Sample data for statistical estimation and hypothesis testing

questions

Observation

Number

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

Disinfection time

(minutes)

Price willing to

pay ($)

Daily revenue of

new product ($)

Customer satisfaction

score (points)

20

21

15

25

22

30

20

33

21

26

20

25

22

24

35

15

13

59

62

15

13

22

20

26

67

45

24

19

18

44

44

36

21

24

23

32

30

41

25

80

81

45

35

55

46

66

85

92

87

86

95

78

94

78

80

86

99

89

82

75

75

75

100

94

77

87

100

97

25

33

82

85

100

90

94

99

95

33

22843

22456

23147

24151

28027

27676

22778

24777

26910

20261

25221

20544

26378

22443

21002

15889

21889

20445

23530

22974

20826

28754

32336

26186

20355

12909

21880

15669

31795

20736

21282

26105

24115

25796

26019

26501

21094

23002

22089

73

64

55

70

85

67

72

45

64

65

45

71

69

71

69

56

68

67

65

79

80

33

81

75

47

45

89

70

87

76

73

45

61

65

81

79

33

61

72

Observation

Number

40

41

42

43

44

45

46

47

48

49

50

Disinfection time

(minutes)

Price willing to

pay ($)

Daily revenue of

new product ($)

Customer satisfaction

score (points)

50

22

23

34

11

68

30

45

72

57

54

85

83

82

122

98

33

33

45

25

90

75

29914

29448

25729

13782

22553

25375

29103

23643

22284

28719

29756

45

80

63

81

76

78

88

86

65

61

71

School of Business Management

2022/23 Semester 1

BM3034 Business Statistics

ICA 3

Individual Assignment Guide

Date of Issue: Monday, 4 Jul 2022 (through NYP LMS)

Date of Submission: Monday, 15 Aug 2022, 2359 hours (through NYP LMS)

Individual Assignment Guide / BM3034 / Page 2

1.

Assignment Outline

This individual assignment constitutes 45% of the overall assessment for the

module, BM3034 Business Statistics. The assignment covers topics on

continuous probability distribution, sampling distribution of the sample means,

statistical estimation and hypothesis testing. You will solve problems in the above

topics and submit a report on how you apply the statistical concepts to facilitate

your decision-making process when conducting a business survey research.

Learners will submit on an individual basis, a typewritten report in MS Word with

supporting appendices on the raw data and statistical output in MS Excel.

2.

Learning Outcomes

After the completion of this assignment, learners will be able to:

•

•

•

3.

Solve problems using concepts on the continuous probability distribution.

Select a representative sample when conducting business survey research

by applying theories of the sampling distribution of the sample means.

Perform inferential statistics on real-life data using statistical estimation and

hypothesis testing techniques.

Requirements

Please approach your tutor if you have any query about the instructions indicated

below:

3.1 Continuous Probability Distribution (25 marks)

Each learner must use one (1) of the following three (3) continuous

probability distribution cases listed below based on the instructions given.

•

For learners whose admission number ends with the numbers

“0,1,2,3” solve Case 1.

•

For learners whose admission number ends with the numbers

“4,5,6” solve Case 2.

•

For learners whose admission number ends with the numbers

“7,8,9” solve Case 3.

Case 1

According to the traffic statistics by LTA, the speed of

vehicles that travel along PIE is normally distributed with a

mean of 88 km/h and a standard deviation of 21 km/h.

Case 2

Based on a health care researcher of a hospital, the height

of female individuals aged 15-25 is normally distributed with

a mean of 159 cm and a standard deviation of 16 cm.

Individual Assignment Guide / BM3034 / Page 3

Case 3

According to a sport & wellness professional, the weight of

male individuals aged 35-45 is normally distributed with a

mean of 72 kg and a standard deviation of 19 kg.

Based on your case assigned, solve the following problems using

continuous probability distribution techniques. Diagram is not needed in

your answer. Write down your answers with appropriate workings in your

report. State clearly the case that you are solving. Example: 3.1

Continuous Probability Distribution Case 1, 2 or 3.

(a)

State the variance and how the normal curve will change when the

mean decreases and the standard deviation increases.

(3 marks)

(b)

Determine with appropriate calculations if you agree or disagree with

the statement that “95.44% of the population items lies within 2

standard deviations of the population mean.”

(4 marks)

(c)

Calculate the amount for the top and bottom kth percentage of the

population, where k is your register number in your class register.

Show all the steps required.

(12 marks)

(d)

Calculate the probability that an individual in the population (X) is

more than 4 standard deviations bigger than the population mean.

Explain if it is possible to find such an individual in the population with

reference to your case scenario.

(6 marks)

3.2 Sampling Distribution of the Sample Means (25 marks)

A survey research is a tool used by businesses to obtain feedback from

their customers, suppliers or employees. One of the requirements to obtain

good feedback from their respondents when conducting a survey is to

select a representative sample for the survey.

For this assignment, you are the business personnel who is conducting a

survey for your company to obtain an estimate on the population mean.

Write a 750-word reflection on how the concepts and theorem(s) taught in

the topic “Sampling Distribution of the Sample Means” can facilitate your

decision-making process in conducting the business survey research, such

as choosing an appropriate sample size for the survey as well as other

considerations, costs and benefits.

Your reflection should provide discussion and explanation for the following

areas:

Individual Assignment Guide / BM3034 / Page 4

(a)

How do the concepts and theorem(s) in the topic “Sampling

Distribution of the Sample Means” influence your decision in choosing

an appropriate (or minimum) sample size for the survey? (10 marks)

(b)

Is a bigger sample better for the survey? Discuss the benefits of

having a bigger sample for the survey with reference to the standard

error. Any possible costs associated with a bigger sample selected?

How do you decide on the sample size for your survey?

(5 marks)

(c)

Besides the knowledge gained in the topic, suggest any three (3)

measures that you can undertake to obtain good feedback from your

respondents when conducting the survey. Be as innovative as

possible and provide reasons and elaborations to support your

suggestions.

(10 marks)

3.3 Statistical Estimation (25 marks)

Each learner must use one (1) of the following two (2) statistical estimation

cases listed below based on the instructions given.

•

For learners whose admission number ends with letters “A” to

“O”, solve Case 1.

•

For learners whose admission number ends with letters “P” to “Z”,

solve Case 2.

Case 1

Covid19 has highlighted the importance of strict hygiene and

more frequent cleaning and disinfection of hotel

accommodation. A hotel is keen to automate the disinfection

process and is evaluating a new cleaning and disinfection

robot for a month. Currently it takes the housekeeping staff

an average of 65 minutes to disinfect a room. The hotel

management aims to reduce the average disinfection time by

half. If the upper confidence limit of the interval estimate on

the population mean disinfection time by the robot does not

meet the target, the robot will not be purchased, vice versa.

A random sample of hotel rooms cleaned by the robot was

selected and the disinfection time was recorded during the

trial month. The data collected is shown in Appendix 1.

Individual Assignment Guide / BM3034 / Page 5

Case 2

A new Italian restaurant wanted to determine the price that it

should charge for its new signature dish, FB Risotto. The

restaurant intended to price the dish at more than $85 and

was concerned about the impact of price on the popularity of

the new dish. To determine the optimum price to charge, a

random sample of potential customers was surveyed on the

price they would be willing to pay for the dish. If the upper

confidence limit of the interval estimate on the population

mean price is above $85, the manager would price the dish

accordingly, vice versa. The data collected is shown in

Appendix 1.

The sample size taken for each learner is n=15+k, where k is your register

number in your class register. For example, if your class register number

is 1, the sample size that you will select is n=15+1=16. Thus, you will select

the first n=16 from the relevant sample data in Appendix 1 and perform the

appropriate calculations. Likewise, if your class register number is 20, the

sample size that you will select is n=15+20=35. Thus, you will select the

first n=35 from the relevant sample data in Appendix 1 and perform the

appropriate calculations.

Based on your case assigned, solve the following problems using statistical

estimation techniques. Diagram is not needed in your answer. Write down

your answers with appropriate workings in your report. State clearly the

case that you are solving. Example: 3.3 Statistical Estimation Case 1 or

2

(a)

Copy the sample data tabulated in appendix 1 and paste them into

MS Excel and perform descriptive statistics on the data using MS

Excel Data Analysis Tool Pak. Refer to the detailed illustration and

instructions on how to perform descriptive statistics from the video

lectures taught in class and in NYP LMS. Save the raw data and the

output of the descriptive statistics on the same worksheet and submit

them in the appendix section.

(2 marks)

(b)

State the point estimates for the population mean and standard

deviation.

(2 marks)

(c)

Calculate the 95% confidence interval for the population mean. Show

all the required calculations.

(9 marks)

(d)

Determine the decision for your case above.

(e)

Suggest how to improve the reliability and precision of the confidence

interval calculated. Calculate the minimum sample size which can

reduce the width of the confidence interval by half.

(9 marks)

(3 marks)

Individual Assignment Guide / BM3034 / Page 6

3.4 Hypothesis testing (25 marks)

Each learner must solve one (1) of the following two (2) hypothesis testing

cases listed below based on the instructions given.

•

For learners whose admission number ends with an odd number

(1,3,5,7,9), solve Case 1.

•

For learners whose admission number ends with an even number

(2,4,6,8,0), solve Case 2.

Case 1

According to a marketing personnel, the daily revenue target

of a new product set by management was $25,000 per day.

The marketing personnel convened a survey to measure the

daily revenue of the new product to determine if the average

actual revenue was below the target. If the average actual

revenue was below the target, more money will be spent on

marketing the new product. The data collected is shown in a

table in Appendix 1. Determine if the population mean daily

revenue of the product was below the target with a

hypothesis test at 1% level of significance. The data collected

is shown in Appendix 1

Case 2

A restaurant was evaluating if its customer service standard

needs to be enhanced. Management had determined that if

the average satisfaction score of its customers fell below 70

80 points, corrective actions would be undertaken. To

measure the satisfaction score of its customers, a survey

was commissioned. The data collected is shown in a table in

Appendix 1. Determine if the average satisfaction score of

its customers fell below 80 points with a hypothesis test at

5% significance level. The data collected is shown in

Appendix 1

The sample size taken for each learner is n=44-k, where k is your register

number in your class register. For example, if your class register number

is 1, the sample size that you will select is n=44-1=43. Thus, you will select

the first n=43 from the relevant sample data in Appendix 1 and perform the

appropriate calculations. Likewise, if your class register number is 20, the

sample size that you will select is n=44-20=24. Thus, you will select the

Individual Assignment Guide / BM3034 / Page 7

first n=24 from the relevant sample data in Appendix 1 and perform the

appropriate calculations.

Based on your case assigned, solve the following problems using

hypothesis testing methodology. Diagram is not needed in your answer.

Write down your answers with appropriate workings in your report. State

clearly the case that you are solving. Example: 3.4 Hypothesis Testing

Case 1 or 2.

4.

(a)

Copy the relevant sample data tabulated in appendix 1 and paste

them into MS Excel and perform descriptive statistics on the data

using MS Excel Data Analysis Tool Pak. Refer to the detailed

illustration and instructions on how to perform descriptive statistics

from the video lectures taught in class and in NYP LMS. Save the raw

data and the output of the descriptive statistics on the same worksheet

and submit them in the appendix section.

(2 marks)

(b)

State the values of the sample mean and sample standard deviation.

(2 marks)

(c)

Determine the conclusion for your case above using a hypothesis

test. Show all the calculations required.

(11 marks)

(d)

Describe type I and II errors.

(e)

Explain the consequences of committing type I and type II errors

respectively. Suggest how to adjust the significance level to minimise

type I and type II errors respectively.

(6 marks)

(4 marks)

Submissions

Report Format

• A written report of not more than 7 pages (excluding cover page and

appendices)

• Arial Font size 12 with single spacing must be submitted by each

individual learner.

• Please assign your file name for submission with the following format:

BM3034_Class_Name_Admin Number e.g.

BM3034_HA_Soh Eazi_1234567A

Your report should clearly label the following parts:

i)

Cover Page: Include a cover page with the assignment title (BM3034 ICA

3: Business Statistics Individual Assignment), name and admission

number of the learner.

Individual Assignment Guide / BM3034 / Page 8

ii)

Continuous Probability Distribution: Solutions for the case assigned to

you.

iii)

Sampling Distribution of the Sample Means: A reflection of not more

than 750 words (inclusive within the 7-page limit) on the topic that consists

of discussion and explanation for the areas required as mentioned above.

iv)

Statistical Estimation: Solutions for the case assigned to you.

v)

Hypothesis Testing: Solutions for the case assigned to you.

vi)

Appendix: providing the raw sample data of the statistical estimation and

hypothesis testing cases assigned and the output of the descriptive

statistics generated by the MS Excel Data Analysis Tool Pak.

Submission through Turnitin in NYP LMS and Due Date

The report is to be submitted through Turnitin latest by Monday,15 Aug

2022, 2359 hours. Turnitin is a cloud-based solution with capabilities in

originality checking using their OriginalityCheck tool. OriginalityCheck allows

your instructor to monitor assignment submissions and identify potential cases

of plagiarism by automatically comparing submissions to an online database of

original content. It is the responsibility of the learners to ensure that the matching

text highlighted in the Turnitin similarity report is properly referenced.

1.

Please read the following guide on how to submit your report in Politemall:

https://help.turnitin.com/feedback-studio/d2l/student/submitting-apaper/submitting-a-paper.htm

2.

Learners can also view the following video to learn how to submit your

report in Politemall:

Late submission and penalties

A penalty of 5% on the base marks to be deducted for each working day of late

submission from the respective assessment marks allocated should the report

be submitted late. Any late submission after 5 working days will be awarded zero

mark.

Plagiarism

Plagiarism is serious matter. Plagiarism is the act of taking and using the whole

or any part of ideas, words or works of other people and passing it off as one’s

Individual Assignment Guide / BM3034 / Page 9

own work, without acknowledgement of the original source. The act of

plagiarism is an offence under NYP Academic Integrity Policy:

https://www.nyp.edu.sg/current-students/academic-matters/nyp-academicintegrity.html. Any act of plagiarism may be construed as academic dishonesty.

A candidate who, after due disciplinary process, is found to have committed an

act that contravenes academic integrity in any assessment of a module would

be liable for disciplinary action under NYP Academic Integrity Policy.

It is also important not to share your or your team’s work with other learner(s) or

team(s). ALL parties involved in any act of plagiarism (including learner(s)

or team(s) who have shared their work with others) would be liable for

disciplinary action under NYP Academic Integrity Policy. If any learner had

asked you to share your work with him/her, it is important to turn down his/her

request and report the incident immediately to your module tutor to safeguard

your integrity.

All content from online or other primary sources should be properly referenced

(even if you are paraphrasing). Learners can use https://www.scribbr.com/apacitation-generator/ or other online citation generator to properly state the source

of the reference (websites, journal articles, books and reports) in the American

Psychological Association (APA) format. The APA format is a writing style and

format for academic documents such as scholarly journal articles and

books. When in doubt, the rule is to acknowledge the source.

A Turnitin Similarity Report generated provides detailed information about the

matches found between a learner’s submitted work and existing sources.

Learners can use the report to review their submissions for originality and identify

the specific areas of their submitted work where proper referencing are required.

Failing to do so may lead to plagiarism being reported in Turnitin.

5.

When an assignment is submitted using Turnitin, the Turnitin Similarity Report is

normally available within 15-30 minutes. However, a slight delay may occur

between the upload and the availability of the Similarity Report during periods of

high usage. Hence, learners are encouraged to submit their report at least one

day before the submission deadline so that they have sufficient time to make any

necessary amendment and resubmission before the submission deadline

expires.

Assessment

The assignment written report carries a total of 100 marks and constitutes 45%

of the overall grade for the module. The breakdown of marks is as follows:

The evaluation criteria for the written report is as follow:

Individual Assignment Guide / BM3034 / Page 10

Continuous Probability Distribution (25 marks)

i)

Correct solutions for the assigned case.

Sampling Distribution of the Sample Means (25 marks)

A coherent reflection of the topic that provides adequate discussion,

elaboration and explanation. The details of the rubrics are attached in

Appendix 2.

Statistical Estimation (25 marks)

i)

Correct solutions for the assigned case.

Hypothesis Testing (25 marks)

i)

Correct solutions for the assigned case.

Individual Assignment Guide / BM3034 / Page 11

Appendix 1

Sample data for statistical estimation and hypothesis testing questions.

Obtain the sample data from the MS Word document named “Appendix 1Sample data for statistical estimation and hypothesis testing questions” in the

NYP LMS.

Individual Assignment Guide / BM3034 / Page 12

Appendix 2-Scoring Rubric of Reflection

Evaluation Criteria

Concepts and

theorem(s) in the

topic and

appropriate

(minimum) sample

size chosen

(10 marks)

Exceed

Expectations

9-10 marks

Concepts and

theorem(s) are all

stated correctly.

Appropriate

(minimum) sample

size chosen is

correct.

Excellent

explanation and

elaboration

provided.

Benefits and costs

of a big sample size

(5 marks)

Meet

Expectations

7-8 marks

Approaching

Expectations

5-6 marks

Below

Expectations

3-4 marks

Inadequate

Concepts and

theorem(s) are

mostly stated

correctly.

Concepts and

theorem(s) are

stated with some

errors.

Concepts and

theorem(s) are

stated with a lot of

errors.

No concept or that

concepts and

theorem(s) are

stated wrongly.

Appropriate

(minimum) sample

size chosen is

correct.

Appropriate

(minimum) sample

size chosen is

correct.

Appropriate

(minimum) sample

size chosen is

wrong.

Appropriate

(minimum) sample

size chosen is

wrong.

Good explanation

and elaboration

provided.

Average

explanation and

elaboration

provided.

Poor explanation

and elaboration

provided.

No/ wrong

explanation and

elaboration

provided.

1-2 marks

5 marks

4 marks

3 marks

2 marks

1 mark

Excellent

explanation and

elaboration of the

benefits and costs

of having a big

sample size.

Good explanation

and elaboration of

the benefits and

costs of having a

big sample size.

Average

explanation and

elaboration of the

benefits and costs

of having a big

sample size.

Poor explanation

and elaboration of

the benefits and

costs of having a

big sample size.

No/ wrong

explanation and

elaboration of the

benefits and costs

of having a big

sample size.

Individual Assignment Guide / BM3034 / Page 13

Decision made on

the sample size to

take with excellent

explanation.

Suggestions on

three measures to

obtain good

feedback from

respondents

Decision made on

the sample size to

take with average

explanation.

Decision made on

the sample size to

take with poor

explanation.

No decision made

on the sample size

to take.

9-10 marks

Decision made on

the sample size to

take with good

explanation.

7-8 marks

5-6 marks

3-4 marks

1-2 marks

All three

suggestions

provided are valid

and innovative.

Most of the

suggestions

provided are valid

and innovative.

Some of the

suggestions

provided are valid

and innovative.

Some of the

suggestions are

invalid.

No suggestion

provided or that

suggestions are

invalid.

Excellent

elaboration on all

three suggestions

provided.

Good elaboration

on the suggestions

provided.

Average

elaboration on the

suggestions

provided.

Poor elaboration

on the suggestions

provided.

No elaboration on

the suggestions

provided.

.

(10 marks)

END

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