Dr. Loizeaux

STAT 350 (Spring 2017) Homework 8 (20 points) 1

Practice Problems: 9.57 (p.412), 9.59 (p.412), 9.99 (p. 423), 9.101 (p.423), 9.103 (p.4.23), 9.125 (p. 433), 9.127 (p.433)

(1 pt.) 1. You are told that a hypothesis test is significant at the 5% level. Given this information,

is the test significant at the 1% level? Please explain your answer. (0.5 pt.) 2. You perform 1100 significance tests using α = 0.05. Assuming that the null

hypotheses is true, how many of the test results would you expect to be statistically significant?

(10.5 pts.) 3. Residential mailboxes in Des Moines, Iowa, should be installed such that the

bottom of the mailbox is 42 inches above the ground. This rule is designed for safety and to accommodate short mail carriers. A random sample of 75 mailboxes in the city was selected. The distance between the bottom of the mailbox and the ground of each mailbox was carefully measured, and the sample mean was 43.22 inches. Assume that the population standard deviation is 7.6 inches. Assume that the underlying distribution is normal.

(0.5 pt.) a) Should a z or t distribution be used for statistical procedures regarding the mean?

Remember to explain your answer. (6 pts.) b) Is there any evidence to suggest the true mean height of mailboxes in Des Moines is

different from 42 inches? Use = 0.05. Include the complete four step hypothesis test including all of the work.

(2 pts.) c) Calculate and interpret the 95% confidence interval for the mean. (1 pt.) d) Explain why parts b) and c) state the same thing. That is, what in part b) is consistent

with what in part c). (1 pt.) e) From the information provided in parts b) – d), do you think the mean height of

mailboxes in Des Moines is different from 42 inches? The precision of the measurement is 1 inch. Please explain your answer. Hint: Think about the practicality of the situation.

(6.5 pts.) 4. Arizona state procurement specifications for instant-dry highway paint indicate that

the paint must dry in less than 60 seconds. A random sample of 40 cans of paint was obtained from a potential seller, and the drying time of each batch was carefully tested. The sample mean was 54.6 seconds with a sample standard deviation of 7.76 seconds. You may assume that the population is normal.

(0.5 pt.) a) Should a z or t distribution be used for statistical procedures regarding the mean?

Remember to explain your answer. (6 pts.) b) Is there any evidence to suggest the mean drying time for this highway paint is less

than 60 seconds? Perform the hypothesis test at a 1% significance level. Include the complete four step hypothesis test including all of the work.

(1.5 pts.) 5. After analyzing a database of over 2 million international telephone calls, Vonage reported that the mean length of all of these calls was 295 seconds. Following an extensive advertising campaign, the company expected the length of international calls to increase. A few months after the ads first appeared, a random sample of 48 calls was obtained. The sample mean was = 306.3 seconds. Assume that the population standard deviation is 52 seconds. (0.5 pt.) a) State the hypotheses that are being tested. Be sure to include both the null and

alternative hypotheses. (1 pt.) b) Find the probability of a type II error if the true mean after call length is μa = 320; that

is, find β(320). Assume that = 0.01.

STAT 350 (Spring 2017) Homework 8 (20 points) 2

Additional Problems: 9.77, 9.79, 9.83, 9.87, 9.95, 9.97, 9.113, 9.119, 9.145, 9.147