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 2,900 miles. Assume a level of significance for testing of 5%, and a random sample of 75 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) What would be the consequences of making a Type II error in this problem?

Our Null Hypothesis is  mean life is at least 25,000 miles

alternative Hypothesis is  mean life of at lmost 25,000 miles

Here consequence of Type II error is we end up accepting tire whose mean life is actually less than 25,000 miles

B) Compute the Probability of making a Type II error if the true population mean is 24,000 miles.

p( Type II error)=p(accep H0 when H1 is true)

p(M>25000/true mean=24000)

=p((M-24000)*sqrt(75)/2,900 >(25000-24000)*sqrt(75)/2,900 )

=p(Z>2.986294)

=0.001

Hence type II error is 1%

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