1) Management at the Kimberly Clark Corporation need to determine how many tissues a package of Kleenex should contain. Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: x̄ = 52, S = 22.

a) Give the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 60.

b) Using the sample information provided, calculate the value of the test statistic. Show your work.

c) Suppose the alternative we wanted to test was H1 : μ < 60. State the correct rejection region for α = 0.05.

d) Suppose the test statistic does fall in the rejection region at α = 0.05. Which of the following conclusions is correct? Justify your choice.

A) At α = 0.05, there is not sufficient evidence to conclude that the average number of tissues used during a cold is 60 tissues.

B) At α = 0.05, there is sufficient evidence to conclude that the average number of tissues used during a cold is 60 tissues.

C) At α = 0.05, there is not sufficient evidence to conclude that the average number of tissues used during a cold is not 60 tissues.

D) At α = 0.10, there is sufficient evidence to conclude that the average number of tissues used during a cold is not 60 tissues.

2) We have created a 95% confidence interval for μ with the result (10, 15).

a) What decision will we make if we test H0 : μ = 16 versus H1 : μ ≠ 16 at α = 0.05? Justify your answer.

A) Reject H0 in favor of H1.

B) Accept H0 in favor of H1.

C) Fail to reject H0 in favor of H1.

D) We cannot tell what our decision will be from the information given.

b) What decision will we make if we test H0 : μ = 16 versus H1 : μ ≠ 16 at α = 0.10? Justify your answer.

A) Reject H0 in favor of H1.

B) Accept H0 in favor of H1.

C) Fail to reject H0 in favor of H1.

D) We cannot tell what our decision will be from the information given.

c) What decision will we make if we test H0 : μ = 16 versus H1 : μ ≠ 16 at α = 0.025?

A) Reject H0 in favor of H1.

B) Accept H0 in favor of H1.

C) Fail to reject H0 in favor of H1.

D) We cannot tell what our decision will be from the information given.

3) The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made.

a) State the appropriate null hypothesis and alternative hypothesis. Explain how you obtain your answer.

b) If she wants to be 99% confident in her decision, what rejection region should she use? Explain how you obtain your answer.

c) Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to be 99% confident in her decision, what decision should she make? Explain how you obtain your answer.

d) Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to be 99% confident in her decision, what conclusion can she make? Explain how you obtain your answer.

e) Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. What is the p-value associated with the test statistic? Explain how you obtain your answer.