Question

A tow truck company suspects that the lifespan 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 = 1300 miles

26579 27965 26868 25070 26488
25834 27355 28039 32237 25523
28331 29103 24439 32850 28942
27474 27618 25645 27497 28183
27475 27697 28524 27704 26873
27232 31633 29363 26857 28017
27396 26982 28007 26293 25828
28256 25679 22594 31000 24208

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