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## Assignment Outline

This individual assignment constitutes 40% 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.

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

• Solve problems using concepts on the continuous probability distribution.
• Select a representative sample when conducting a 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.

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 3.1 (i)(a).For learners whose admission number ends with the numbers “4,5,6” solve Case 3.1 (i)(b). For learners whose admission number ends with the numbers “7,8,9” solve Case 3.1 (i)(c).
• The speed of vehicles that travel along ECP is normally distributed with a mean of 90 km/h and a standard deviation of 15 km/h.
• The height of female individuals aged 20-30 is normally distributed with a mean 162 cm and a standard deviation of 9 cm.
• The weight of male individuals aged 30-40 is normally distributed with a mean 76 kg and a standard deviation of 11 kg.
• Based on your case assigned from above, solve the following problems using continuous probability distribution techniques. Diagram is not needed for this section.

(a) State the mean, standard deviation and variance. (3 marks)

(b) Determine with appropriate calculations if you agree or disagree with the statement that “Less than 5% of the population items lies beyond 2 standard deviations from the population mean.”

(c) Calculate the amount for the top and bottom kth percentage of the population, where k is your register number in your class register.

(12 marks)

(d) Calculate the probability that an individual in the population (X) is more than 5 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

• Write down your answers with appropriate workings in your report. State clearly the case that you are solving. Example: Continuous Probability

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 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:
• 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)
• 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? (6 marks)

• 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. (9 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 3.3 (i)(a).For learners whose admission number ends with letters “P” to “Z”, solve Case 3.3 (i)(b). 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. On the other hand, 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.
• E-commerce and online shopping have become extremely popular. According to a marketing personnel of an online store, the daily sales target for a new product listed on the store is \$5,000 per day. The marketing personnel convened a survey to measure the daily sales of the new product to determine if the actual sales meets with the target. If the upper confidence limit of the interval estimate for the population mean does not meet the target, the new product will be delisted from the online store, vice versa. A random sample of daily sales for the new product was selected and recorded during the trial period. The data collected is shown in a table in Appendix 1.
• A hotel has started a staycation marketing campaign and wants to determine if the campaign has been successful in increasing the average spending per room booking. The marketing director considers the campaign to be successful if the average spending per room booking exceeds \$500. To determine if this was the case, a random sample of recent spending per room booking was tracked and recorded in a table in Appendix 1.If the upper confidence limit of the interval estimate for the population mean spending per room booking does not meet the target, the staycation marketing campaign will be discontinued, vice versa.
• Based on your case assigned from above, solve the following problems using statistical estimation techniques. Diagram is not needed in this section.

(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? (6 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.

• 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 3.4 (i)(a).For learners whose admission number ends with an even number (2,4,6,8,0), solve Case 3.4 (i)(b). 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. On the other hand, 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.
• The F&B manager of a popular restaurant is concerned of the long waiting time by its customers. The average waiting time of customers is 60 minutes before being served. After implementing the customer service improvement plan (increasing the headcount and revamping the queue system), the F&B manager claimed that the average waiting time of its customers had shortened by more than 20%. If the plan does not meet the target, the restaurant will implement a new customer service improvement plan. The waiting time of a random sample of the restaurant customers was tracked and shown in a table in Appendix 1. Determineif the average waiting time of the restaurantcustomers had shortened by more than 20% with a hypothesis test at 1% level of significance.
• A hotel is concerned that the average satisfaction score of its guests had fallen following recent restrictions of the use of hotel facilities. If the average satisfaction score of its guests fell short of its target of 80 points by more than 15%, corrective actions will be taken. To measure the satisfaction level of its guests, a survey was commissioned. The data collected from a random sample of hotel guests is shown in a table in Appendix 1. Determineif the average satisfaction score of its guests had fallen short of its target of 80 points by more than 15% with a hypothesis test at 5% significance level.
• Using the relevant sample data tabulated for the above cases in appendix 1, solve the assigned case using hypothesis testing methodology. Diagram is not needed in this section.
• 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 BlackBoard. 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 steps required. (11 marks)

(d) Describe type I and II errors. (4 marks)

(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