# A tire manufacturer produces tires that are believed to have a mean life of at least 25,000 miles when

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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

Claim: 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.

That is mean life  $\geq&space;25000$ miles.

So null hypothesis H0 and Ha would be :

$H_{0}:&space;\mu&space;\geq&space;25000$  Vs    $H_{a}:&space;\mu&space;<&space;25000$

1. A) What would be the consequences of making a Type II error in this problem?

Type II Error = Fail to reject H0 , when actually it is False.