## Section 1 Assignment Outline

This Assignment constitutes 45% of the overall assessment for the learning unit, BM4345 Applied Statistics for Business.

The assignment covers topics on discrete and continuous probability distribution, sampling distribution of the sample means, statistical estimation and hypothesis testing and statistical concepts covered in previous topics.

Learners will produce a report on how you apply the concepts to facilitate your decision making process when conducting business survey research in the following areas:

- Solving business problems using concepts of discrete probability distributions.
- Choosing an appropriate sample size for the survey as well as other considerations, costs and benefits.
- Conducting appropriate statistical estimation and hypothesis tests on the population mean values to solve business problems.

Please refer to section 3 for details of the report requirements.

Learners will submit on an individual basis, a typewritten report in MS Word and statistical output in MS Excel.

## Section 2 Learning Outcomes

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

- Solving business problems using concepts of discrete probability distributions.
- Select a representative sample when conducting business survey research by applying theories of sampling distribution of the sample means.
- Perform inferential statistics on real-life data using statistical estimation and hypothesis testing techniques.

## Section 3 Requirements

Each learner must complete the following tasks and prepare a written report on your analysis and findings.

### Section 3.1 Reflection (35 marks)

## Case

You are the customer service director of a mid-tier hotel chain, named “Stay here for Best Memories” (SBM). The hotel chain has a mission statement to provide memorable experiences for its two (2) target market segments- business and leisure travellers. To obtain up-to-date feedback from hotel guests, a hotel experience survey is conducted electronically to obtain feedback from its guests about their stay at the hotel. The customer service director will update management on the key findings every quarterly. Timely and cost-effective survey findings are the key priorities of the customer service director.

### Survey Objectives

1. Compare the rating scores and qualitative feedback across different two (2) target market segments-business vis-à-vis leisure on their overall experience, room cleanliness & comfort and staff service & professionalism. 2. Identify areas of improvement and increase business opportunities for the hotel.

### Survey Questionnaire (Partial)

Q1. Please rate the following aspects of your stay at our hotel on a scale from 1 to 5.

- Overall experience
- Room Cleanliness & Comfort (e.g., bed quality, temperature control) (c) Staff Service & Professionalism (e.g., responsiveness, helpfulness)

### Tasks

Write a 900-word reflection on how the concepts and theorem(s) taught in the topic “Sampling Distribution of the Sample Means” and “Discrete Probability Distribution” can facilitate your decision-making process in conducting the hotel experience survey, 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:

## (a) Sampling Plan

If the population standard deviation of the guest overall experience rating score is 1.5 points, would you advise the customer service director to randomly (i) select a hotel guest; (ii) select a sample of 20 hotel guests; (iii) select a sample of 30 hotel guests; or (iv) select a sample of 40 guests for each customer segment in the survey above? ** Evaluate** the pros and cons of each of the 4 options above with appropriate calculations.

**the sampling plan to meet the survey objectives above.**

__Determine__## (b) Survey Instrument

** Amend** the survey questionnaire above and

**further questions and/or sections to meet the survey objectives fully and**

__add__**on how you would analyse the questions in your survey questionnaire and present the key findings for the quarterly report to management.**

__elaborate__## (c) Hotel Guest Complaint Situation

Based on past data, the number of complaints received from hotel guests follow a Poisson Distribution with an average of 2 complaints per day. A day with more than 4 complaints is considered a high-complaint day. If the probability that there are more than 1 high-complaint days in a week exceed 0.05, it would warrant management’s attention. With appropriate calculations, ** determine** if the complaint situation in the hotel warrant management’s attention.

### Section 3.2 Statistical Estimation (35 marks)

Solve the following case using statistical estimation techniques. **Diagram is not needed in your answer**. Write down your answers with appropriate workings in your report. ** **

## Case

Miss Caring Cher is a success coach and chief researcher of a company, Strong Body & Mind (SBM), whose mission is to deliver enriching sport & wellness programmes for youth. She is concerned about the health & fitness, mental wellness and gaming addiction problem of youth today. A study was commissioned by Miss Cher to estimate the population mean weekly time taken for exercise by youth. A random sample of youth (aged 17 to 21) was surveyed and the sample data was collected for the study. Miss Cher will be concerned if the upper confidence limit of the interval estimate is lower than 2 hours. Please refer to **Appendix **1 on how to access these data.

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

**. For example, if your class register number is**

*your register number in your class register***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.

**REGISTER NUMBER IS 18.**

## Tasks

- 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. Save the raw data and the output of the descriptive statistics on the same worksheet and submit them as a MS Excel file.
the values of the sample mean and sample standard deviation.__Obtain__the 95% confidence interval for the population mean weekly time taken for exercise by youth and__Calculate__if Miss Cher should be concerned.__explain__all the required calculations.__Show__

the minimum sample size which can reduce the width of the confidence interval by one-third.__Calculate__

- Miss Cher’s research has shown that a meaningful and successful time in school by youth depends on the following factors outlined by the following regression equation:

Meaningful and successful time in school by youth

= 2.8Attitude + 3.3Effort + 0.5Ability +1.9Time taken for exercise -1.5Time taken for gaming.

** Analyze** the equation above and

**a report (maximum 300-word count) for Miss Cher on how she can advise youth today on the concrete steps to take to lead a meaningful and successful time in school.**

__prepare__### Section 3.3 Hypothesis Testing (30 marks)

Solve the following case using hypothesis testing methodology. **Diagram is not needed in your answer.** Write down your answers with appropriate workings in your report.

## Case

An earlier study revealed that a typical shopper spent an average of 65 minutes at a shopping mall. The manager of the shopping mall wants to conduct a hypothesis test to determine if the average time spent by shoppers at the shopping mall has dropped significantly as compared to previous study. He wants to use the results of the hypothesis test and other practical considerations to decide whether to renovate the shopping mall to increase foot traffic and profitability for the mall. The manager’s primary concern is to avoid a drop in mall profitability due to decrease in average shopping time. A random sample of shoppers was surveyed and the time spent at the mall was recorded and shown in a table in Appendix 1. ** Determine **the conclusion of the hypothesis test at 5% significance level.

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

**. For example, if your class register number is**

*your register number in your class register***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 first n=24**from the relevant sample data in Appendix 1 and perform the appropriate calculations.

**REGISTER NUMBER IS 18.**

## Tasks

- 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. Save the raw data and the output of the descriptive statistics on the same worksheet and submit them as a MS Excel file.
the values of the sample mean and sample standard deviation.__Obtain__the conclusion for the hypothesis test.__Determine__all the steps required.__Show__ the consequences of type I and type II errors for the hypothesis above and__Discuss__the manager how to adjust the significance level of the hypothesis test based on his primary concern.__advise__- In the above case, there is a requirement for practical considerations besides the conclusion of the hypothesis test before making the decision on the mall renovation plan.
two (2) practical considerations the manager should have examine before making the decision.__Discuss__

### Section 4 Submissions

## Section 4.1 Report Format

A written report of **not more than 9 pages **excluding cover page– Arial Font size 12 with single spacing must be submitted by each learner. The report should consist of the following parts:

### 1. Cover Page

Include a cover page with the assignment title (BM4345 ICA 3: Applied Statistics for Business Individual Assignment), name and admission number of the learner.

### 2. Main Discussion

Refer to section 3 above for the requirements which are to be answered. The summarised guides to the questions are indicated below:

Discrete Probability Distribution and Sampling distribution of the sample means • A reflection of not more than 900 words. Statistical Estimation

- Solutions and elaborations

Hypothesis testing

- Solutions and elaborations

Output of the descriptive statistics generated by the MS Excel Data Analysis Tool Pak. The **dataset and MS Excel output** must be submitted together in a **single MS Excel file** with the **main report in a single MS Word file.**

Name all your documents submitted in the format “**BM4345_ICA3_Class_ _Name_Admin Number**”.

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. Follow this Guide and video on how to submit your report in NYP LMS Turnitin.

## Section 4.3 Rules and Penalties for Late Submission of Assignments and Project Deliverables

The following rules and penalties apply to assignments and project deliverables submitted after the due date:

**Late submissions within 5 calendar days of the due date:**

- If the learner
**passes**the assignment/project, the awarded mark will be**capped at 50%**of the base score for that assignment/project component. - If the learner
**fails**the assignment/project, a**failing score**will be awarded for that assignment/project component.

**Late submissions more than 5 calendar days after the due date:**

- The learner will receive a score of zero for that assignment/project component, regardless of the work’s quality.

**Section 4.4 Plagiarism and Use of Generative Artificial Intelligence (AI).**

As agreed upon in the **Academic Integrity Policy Acknowledgement** you signed at the start of the semester, it is imperative that you adhere to the principles of academic honesty.

## Responsible AI Use for Assessment (AI use allowed + Citation)

In this learning unit, students have the option to use artificial intelligence (AI) for assignments or projects based on their assessment of whether it supports their learning objectives. Use of AI is permitted as a learning tool but is not required or expected.

Students are trusted to utilise AI ethically and responsibly. However, it is crucial to recognise the limitations of these tools. Students must critically evaluate and verify all AI-generated information, data and facts to ensure accuracy and truthfulness. Students are fully accountable for the integrity of the content they submit.

** Citation**. If incorporating AI-generated material, students must clearly label it as such. In-text attributions and references should follow APA style guidelines.

Presenting AI content as one’s own work, fabricating sources, or failing to disclose AI use all constitute academic misconduct and will result in serious disciplinary action. When in doubt, err on the side of over-disclosure of AI use.

## Section 5 Assessment Components

This assignment carries a total of 100 marks and constitutes 45% of the overall grade for the module. The breakdown of marks is as follows:

Component | Marks |

Reflection | 35 |

Statistical Estimation | 35 |

Hypothesis testing | 30 |

Total | 100 |

## Appendix 1 Sample data for hypothesis testing cases

**Refer to attached word document (Appendix 1-Sample data for statistical estimation and hypothesis testing cases) for the sample data to be used for 3.2 and 3.3.**

## Appendix 2 Written Report Rubric

## 3.1 Scoring Rubric of Reflection

Evaluation Criteria | A | B | C | D | F |

Sampling Plan (10 marks) | 8 – 10 | 7 – 7.9 | 6 – 6.9 | 5 – 5.9 | 0 – 4.9 |

Correct sampling plan with appropriate calculations made on the sample size to take. Excellent, comprehensive, and clear explanation of the pros and cons of each option. | Correct sampling plan with appropriate calculations made on the sample size to take. Good explanation of the pros and cons of each option. Improvement in explanation required in terms of clarity and comprehensiveness. | Correct sampling plan with appropriate calculations made on the sample size to take. Explanation of the pros and cons of each option needs to be improved. Some omissions, errors, and ambiguity in the explanation. | Wrong/no sampling plan and wrong/no calculations made on the sample size to take. Explanation of the pros and cons of each option needs to be greatly improved. A lot of omissions, errors and ambiguity made in the explanation. | Wrong/no sampling plan and wrong/no calculations made on the sample size to take. Wrong/No explanation of the pros and cons of each option. | |

Survey Instrument (15 marks) | A | B | C | D | F |

12 – 15 | 10.5 – 11.9 | 9 – 10.4 | 7.5 – 8.9 | 0 – 7.4 | |

Very good questions added to the survey questionnaire to meet the objectives fully. Survey questionnaire is | Good questions added to the survey questionnaire to meet the objectives fully. Slight improvement in | Questions added to the survey questionnaire. However, they do not meet the objectives fully. | Questions added are not original. They do not meet the objectives fully. A lot of improvement in | No question added or questions added are not original. They do not meet the objectives fully. Survey | |

complete and professional. Analysis methods for the different question types are correct. Useful key findings suggested and well elaborated, displaying excellent thought process. | completeness and professionalism of survey questionnaire. Analysis methods for the different question types have slight errors. Somewhat useful key findings suggested but slight improvement in elaboration required. | Some improvement in completeness and professionalism of survey questionnaire. Analysis methods for the different question types have errors. Some findings suggested but some improvement in elaboration required. | completeness and professionalism of survey questionnaire. Analysis methods for the different question types have a lot of errors. Some findings suggested but not original. A lot of improvement in elaboration required. | questionnaire is incomplete and unprofessional. questionnaire. Analysis methods for the different question types have a lot of errors. No finding suggested or findings suggested are not original. No / incorrect elaboration. | |

Hotel Guest Complaint Situation (10 marks) | A | B | C | D | F |

8 – 10 | 7 – 7.9 | 6 – 6.9 | 5 – 5.9 | 0 – 4.9 | |

Correct conclusion reached. All calculations correct. Steps shown clearly. | Correct conclusion reached. Slight errors in calculations. Slight improvement in clarity of steps shown. | Correct conclusion reached but not linked to calculations. Some errors in calculations. Some improvement in clarity of steps. | Correct conclusion reached but not linked to calculations/ Incorrect conclusion. A lot of errors in calculations. A lot of improvement in clarity of steps. | Correct conclusion reached but not linked to calculations/ Incorrect conclusion. A lot of errors in calculations/ No calculation shown. A lot of improvement in clarity of steps. |

## 3.2 Scoring Rubric of Statistical Estimation

Evaluation Criteria | A | B | C | D | F |

Statistical Estimation (10 marks) | 8 – 10 | 7 – 7.9 | 6 – 6.9 | 5 – 5.9 | 0 – 4.9 |

Output of the descriptive statistics submitted in MS Excel. Sample mean and standard deviation calculated correctly. Statistical estimation done correctly with all steps shown clearly. Correct conclusion with clear reason provided. | Output of the descriptive statistics submitted in MS Excel. Sample mean and standard deviation calculated with a few mistakes. Statistical estimation done correctly. A few steps not shown clearly. Correct conclusion with reason provided. | Output of the descriptive statistics submitted in MS Excel. Sample mean and standard deviation calculated with some mistakes. Statistical estimation done with some mistakes. Some steps not shown. Correct conclusion but reason is ambiguous. | Output of the descriptive statistics submitted in MS Excel. Sample mean and standard deviation calculated with many mistakes. Statistical estimation done with many mistakes. Many steps not shown. Wrong conclusion Wrong reason. | Output of the descriptive statistics not submitted in MS Excel. Sample mean and standard deviation calculated wrongly. Statistical estimation done wrongly or not done. No/wrong conclusion. No/wrong reason. | |

Minimum sample size (10 marks) | A | B | C | D | F |

8 – 10 | 7 – 7.9 | 6 – 6.9 | 5 – 5.9 | 0 – 4.9 | |

Minimum sample size calculated correctly with all steps shown clearly. | Minimum sample size calculated correctly. A few steps not shown clearly. | Minimum sample size calculated with some mistakes. Some steps not shown. | Minimum sample size calculated with many mistakes. Many steps not shown. | Minimum sample size calculated wrongly or not done. | |

Report (15 marks) | A | B | C | D | F |

12 – 15 | 10.5 – 11.9 | 9 – 10.4 | 7.5 – 8.9 | 0 – 7.4 | |

Concrete steps and advice are valid, original, linked to the case and cover all the areas. Excellent elaborations provided. | Concrete steps and advice are largely valid, original and covers all the areas. Slight improvement in clarity and linkage to the case. Good elaborations provided. | Only some steps and advice are valid and original. Only some areas are covered. Some improvement in clarity and linkage to the case required. Average elaborations provided. | Most of the steps and advice are invalid and not original. Most areas are not covered. Much improvement in clarity and linkage to the case required. Poor elaborations provided. | No/ invalid/ unoriginal steps or advice provided. No/ very poor elaboration provided. |

## 3.3 Scoring Rubric of Hypothesis testing

Evaluation Criteria | A | B | C | D | F |

Hypothesis Test (15 marks) | 12 – 15 | 10.5 – 11.9 | 9 – 10.4 | 7.5 – 8.9 | 0 – 7.4 |

Output of the descriptive statistics submitted in MS Excel. Sample mean and standard deviation calculated correctly. Hypothesis test done correctly with all steps shown clearly. Conclusion stated clearly and correctly in the hypothesis test. | Output of the descriptive statistics submitted in MS Excel. Sample mean and standard deviation calculated with a few mistakes. Hypothesis test done correctly. A few steps not shown clearly. Conclusion stated correctly in the hypothesis test. | Output of the descriptive statistics submitted in MS Excel. Sample mean and standard deviation calculated with some mistakes. Hypothesis test done with some mistakes. A few steps not shown. Conclusion stated in the hypothesis test with some mistakes. | Output of the descriptive statistics submitted in MS Excel. Sample mean and standard deviation calculated with many mistakes. Hypothesis test done with many mistakes. Many steps not shown. Conclusion stated in the hypothesis test with many mistakes. | Output of the descriptive statistics not submitted in MS Excel. Sample mean and standard deviation calculated wrongly. Hypothesis test done wrongly. Conclusion stated wrongly in the hypothesis test. | |

Type I and Type II errors | A | B | C | D | F |

4 – 5 | 3.5 – 3.9 | 3– 3.4 | 2.5 – 2.9 | 0 – 2.4 | |

(5 marks) | Consequences of errors stated clearly and correctly. Advice provided is correct. | Consequences of errors stated correctly. Slight improvement in clarity. Advice provided is correct. | Consequences of errors stated unclear or with some mistakes. Advice provided is correct. | Consequences of errors stated with many mistakes. Advice provided is wrong. | No/wrong consequences of errors stated. No/wrong advice provided. |

Practical considerations and elaborations (10 marks) | A | B | C | D | F |

8 – 10 | 7 – 7.9 | 6 – 6.9 | 5 – 5.9 | 0 – 4.9 | |

All two practical considerations provided are valid, original and linked to the case. Excellent elaborations provided. | All two practical considerations provided are largely valid and original. Slight improvement in clarity and linkage to the case. Good elaborations provided. | Only one practical consideration provided is valid and original. Some improvement in clarity and linkage to the case required. Average elaborations provided. | Only one practical consideration provided is valid and original. Much improvement in clarity and linkage to the case required. Poor elaborations provided. | No/ invalid/ unoriginal practical considerations provided. No/ very poor elaboration provided. |

**END**