© Patrick J. Farrell (2017) STAT 2606 R – Assignment #8 Due Tuesday, July 25, before 3 pm INSTRUCTIONS: I. Assignments are to be uploaded to the course website on cuLearn as a single legible PDF file by the above due date and time. No late assignments will be accepted without sufficient advanced notice and a legitimate, documented reason. II. You must show and explain all of your work. No credit will be given for answers without justification. III. This assignment is intended to represent your individual knowledge. It is not a group assignment. 1. Of interest to many online retailers are gender-based differences in shopping preferences. A random sample of 15 males yielded a mean monthly expenditure of $352 with a standard deviation of $95, while an independent random sample of 10 females produced a mean monthly expenditure of $310, with a standard deviation of $80. Assume that the monthly online expenditures of both males and females follow a normal distribution. (a) Calculate the ratio of the maximum sample variance to the minimum sample variance. Does it appear that the population variances are equal or unequal? Explain. (b) Construct the appropriate 95% confidence interval for the difference in the mean monthly online expenditures of males and females, and interpret your result. Make sure to clearly identify which gender is identified as Population 1, and which is defined as Population 2. For parts (c) through (e), explain how you would calculate the interval differently in part (b). It is not necessary to calculate the interval, just write out the formula you would use, and substitute in all values. (c) The sample standard deviations are 120 and 60 instead of 95 and 80. (d) The standard deviations of 95 and 80 are the true population standard deviations, not sample results. (e) The sample sizes are each 500 instead of 15 and 10. (f) For each part (b) through (e), explain whether it is necessary to assume that the mean monthly online expenditures of males and females are normally distributed. 2. A city official wishes to know if a new advertising campaign to make residents aware of the danger of driving after drinking has been effective. She counts the number of drivers who have been stopped with more alcohol in their system than the law allows for each day of the week in the week before, and in the week one month after the campaign starts. The results were as follows. Day: Monday Tuesday Wednesday Thursday Friday Saturday Sunday Before: 5 4 2 4 6 14 6 After: 2 0 2 1 8 7 7 (a) Explain why this is a paired design. (b) Compute a 90% confidence interval for the mean difference in the number of drivers with too much alcohol in their system before and after the advertising campaign, and interpret your result. (c) Does it appear that the campaign was effective? Explain. (d) What assumptions are necessary to validate the result in (b)? Explain. © Patrick J. Farrell (2017) 3. Now that the penny has disappeared, suppose that independent random samples of 500 men and 500 women yielded 275 males and 240 females in favour of eliminating the nickel. (a) Compute an approximate 99% confidence interval for the difference in the proportions of males and females who are in favour of eliminating the nickel, and interpret your result. Be sure to clearly identify which gender is identified as Population 1, and which is defined as Population 2. (b) Justify the validity of your approach in part (a).

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