A tire manufacturer produces tires that are believed to have a mean life of at l

Question

A tire manufacturer produces tires that are believed to have a mean life of at least 25,000 miles when the production process is working correctly. Based on past experience, the population standard deviation of the lifetime of the tires is 3,500 miles. Assume a level of significance for testing of 5%, and a random sample of 100 tires: A) What would be the consequences of making a Type II error in this problem? B) Compute the Probability of making a Type II error if the true population mean is 24,000 miles.

Explanation / Answer

a) A type II error is retaining a false null hypothesis. Here the consequence of the type II error would be incorrectly accepting the fact that the mean life of the tires is at least 25,000 miles even though it is less than that.

b) As we are doing the test at a significance level of 0.05, the probability of incorrectly retaining the false null hypothesis is defined as the level of significance and therefore would be 0.05 here

Therefore 0.05 is the required probability of making a type II error here.

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