Application of statistics assignment

É C O L E D E G E S T I O N T E L F E R S C H O O L O F M A N A G E M E N T

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ADM 2304 – ASSIGNMENT 1 Due date: Sunday, February 7 2021 at 11:30 pm (Brightspace). Instructions: • You may use Minitab, MS Excel or other software for any calculations. However, you must

show your manual calculations when asked. You may paste your output onto your assignment to show your use of software; however, this output does not replace any of the steps outlined below. This means that answers that are exclusively software output may receive only partial marks. Include software output when asked to confirm results.

• If you are performing a hypothesis test, make sure you state the hypotheses, the level of significance, the rejection region, the test statistic (and/or p-value, if requested), your decision (whether to reject or not to reject the null hypothesis), and a conclusion in managerial terms that answers the question posed. These steps must be completed in addition to any software output.

• The data for this homework assignment can be found in the files Assign1Data.mpx and Assign1Data.xlsx.

• Your assignment must be typed and uploaded to Brightspace in one single pdf file. You may upload several files, but only the most recent submission prior to the deadline will be graded. You must start each question on a different page and answer the questions in order. Students who fail to follow these instructions will be penalized with 10% of the marks (for example, if the assignment is marked out of 50, the penalty will be 5 marks).

• Late submissions will be accepted according to the late submission policy discussed in class and posted on Brightspace.

• Remember to include your integrity statement. Assignments submitted without a signed integrity statement will not be graded.

For each question below, first show your manual computations and then use software to confirm your results. Also, don’t forget to check that the required conditions are satisfied. Question 1 – Electronic Appliances Warranties (15 Marks) Marketing companies widely use surveys in order to monitor the opinions of the consumers. Last year, a survey was undertaken to ask consumer about who buys different warranties for electronic appliances. Of a sample of 1,100, 56% indicated that they would buy the warranty. This year, another survey of 800 consumers revealed that 46% will buy the warranty. a) Test whether there is sufficient evidence to conclude that the popularity of warranties

for electronic appliances has decreased. Use a 5% significance level and the critical value approach.

b) Compute the p-value associated with the hypothesis test above and explain how it confirms the conclusion reached through the critical value approach in part a).

c) Test whether there is sufficient evidence to conclude that the popularity of warranties for electronic appliances has decreased by more than 5%. Use a 5% significance level.

d) Calculate the appropriate one-sided 95% confidence interval for the decrease in the percentage of people who buy warranties for electronic appliances between last year and this year. Is this interval consistent with your conclusion in parts a) and b) above? Explain.

Question 2 – Disability Insurance Products (15 Marks) An insurance company that sells different life insurance policies is investigating expanding its “disability insurance” products. To help determine the extent and type of offerings, the company needs to know its target market. A survey of 320 adults was drawn, and each person was asked to choose his/her preferred new policy. The survey results can be found in the dataset insurance. The response codes are: (1) just life insurance with a 2% discount; (2) just disability insurance with a 2% discount; (3) life and disability insurance with a 3% discount; and (4) life and health insurance with a 5% discount. a) Compute the sample target market defined as the sample proportion of adults who chose

“disability insurance with a 2% discount” as their preferred new policy. b) Compute the standard error of the target market. c) Test whether the target market is larger than 35%. Use a 10% significance level and the

p-value approach. e) Construct the appropriate one-sided approximate 90% confidence interval for the target

market. Is this interval consistent with your conclusion in parts c) above? Explain. d) What sample size is needed if the company wishes to be 98% confident that their

estimate is within 0.02 of the true target market value?

Question 3 – Waiting Times (20 Marks) A manager of a large grocery store wants to increase the customer service satisfaction rate. He is thinking about giving a 5% discount to customers who wait in line more than 8 minutes. However, to get a better idea about the current waiting times, she hired a student to measure the time spent by customers waiting in line. Using a stopwatch, the student determined the amount of time between the time a customer joined the line and the time he or she reached the teller. The times for a random sample of 50 customers were recorded in the dataset waiting_time. a) Examine a boxplot and a histogram of the Time variable. Display these two plots and

explain if you would expect the means of all possible random waiting time samples of size 50 from the costumer population to follow a normal distribution.

b) Compute the sample mean and the standard error of the mean. Answer the following questions regardless of your answer to part a). In other words, assume that all the required conditions are satisfied. c) The store manager would like to determine whether there is enough evidence suggesting

that the mean waiting time for the grocery store’s customers is less than 6 minutes. Conduct the corresponding hypothesis test using a 10% significance level and the p-value approach.

d) Construct the appropriate one-sided 90% confidence interval for the true mean waiting time for the grocery store’s customers. Is this interval consistent with your conclusion in parts c) above? Explain.

e) How large a sample should it be to estimate the mean waiting time for the grocery store’s customers with a margin of error of 0.34 and a 90% confidence? Assume that the waiting time standard deviation is 2.86 minutes.

Good Luck!