STAT 350 (Spring 2017) Homework 8 (20 points + 1 point BONUS) 1 Note: To determine the decision in all hypothesis tests, you need to calculate the p-value. For z-tests, it is required to use the tables from the book. For t-tests, you can not use the tables in the book. The recommended method is to use the internet (google online p value t test). No matter what method that you use, remember to use the degrees of freedom from class, not what is mentioned on the web page and/or calculator manual. 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 900 significance tests using = 0.01. Assuming that the null hypotheses is true, how many of the test results would you expect to be statistically significant? (9.5 pts. 3. The left outside panel of an apartment-size, frost-free refrigerator is designed to have width 23.625 inches. Each hour, 10 such panels are randomly selected from the assembly line and carefully measured. If there is any evidence that the mean width is different from 23.625 inches, the assembly line is shut down for cleaning and inspection. During a specific hour of operation the sample mean is 23.7 inches and the sample standard deviation is 0.15 inches. Suppose the distribution of panel widths 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) Should the assembly line be shut down? 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). (7.5 pts. + 1 pt. BONUS) 4. Jack Keef General Motors, an automobile dealer in Lincoln, Nebraska, advertised a $9.99 40-point safety checkup for any car and claimed that the service department would finish the job in less than 30 minutes. A local newspaper reporter selected a random sample of 58 customers who took advantage of the dealer's offer and found the sample mean time to complete the safety checkup was 32.2 minutes. Assume that the population standard deviation is 5.7 minutes. (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 time to complete the safety checkup is greater than 30 minutes? Perform the hypothesis test at a 1% significance level. Include the complete four step hypothesis test including all of the work. (1 pt.) c) Assume that the appropriate confidence bound is 30.45 minutes, do you think that the true mean time to complete the safety checkup is greater than 30 minutes if the dealership only records the time to the nearest minute? Please explain your answer. Hint: Think about the practicality of the situation. (1 pt. BONUS) d) Which confidence bound, upper bound or lower bound, was used in part c)? Please explain your answer. You will receive 0 points if you do not include an explanation or your explanation includes the results from a calculation. STAT 350 (Spring 2017) Homework 8 (20 points + 1 point BONUS) (1.5 pts.) 5. Based on test results,Speedtest.net publishes an Internet download index for countries all over the world. In July 2013, the mean download speed for the entire world was 13.91 Mbps. A random sample of 14 states was obtained and the download index for each was recorded. The sample average of these states was 17.86 Mbps. Is there any evidence to suggest that the download speed for the United States is greater than for the entire world? Assume the underlying population is normal and that = 3.4. (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 the type II error if the true mean state download speed is a = 17; that is, find (17). Assume that = 0.01. Additional Problems: 9.77, 9.79, 9.83, 9.87, 9.95, 9.97, 9.113, 9.119, 9.145, 9.147 2