Question

A tow truck company suspects that the useful life of certain tires is less than the 28,000 miles they were offered. To verify if its suspicion is true, the company purchases 40 tires, places them in its trucks and measures the life of each one. The results are presented in the rate below.

Presumed known standard deviation = 1200 miles

28965 27531 30211 27700 29191
27218 31246 26151 28453 28753
27613 28560 27106 29395 28852
28164 26220 30894 25910 26247
26767 29664 31536 30671 26811
29516 29096 30185 29537 28135
27768 25767 28601 27726 28601
30598 28196 28939 26414 24601

If we perform a hypothesis test with α = 0.1,

a. What can we conclude? Is the company correct in its suspicions? Respond based on evidence - Clearly define hypotheses, areas of acceptance and rejection, test statistic and CONCLUDE in full sentence

b. If we wanted to construct a confidence interval for µ with an error of not more than 25 miles, what sample size should we use?

c. If the actual average is 27,800 miles, what would be the probability of making a type II error? What would it mean in this case to make a type II error?

Answer 1

The critcal vale and the p value is obtained from STATKEY (images attached for reference). We compute the test statistic using the formula mentioned. The sample size is obtained from the Margin of error formula mentioned.