I\'m working through several assignment questions and want to make sure that I a

Question

I'm working through several assignment questions and want to make sure that I am solving them correctly. Can you please assist me with the below question.

A tire company has developed a new tread design. To determine if the newly designed tire has a mean life of 60,000 miles or more, a random sample of 16 tires is tested. The mean life for the samples is 60,749 miles, with a sample deviation of 1550 miles. Test the hypothesis (a) Compute the test statistic and its P-value. Can be rejected at ? (b) What is the power of the 0.01 level test in (a) if the true mean life for the new tread design is 61,000 miles? (c) Suppose that at least 90% power is needed to identify a tread design that has a mean life of 61,000 miles. How many tires should be tested?

Explanation / Answer

Solution:

a) P-value = P(x? > 60,749|H0: ? = 60,000)
= P(x? - 60,000/1550/sqrt(16) > 60,749 - 60,000/1550/sqrt(16)|H0: ? = 60,000)
= P(Z > 1.93) = 0.0268 < ? = 0.05
So we reject H0.

b) Power = P(x? - 60,000|H0: ? = 61,000)
= P(x? - 61,000/1550/sqrt(16) + 61000 - 60,000/1550/sqrt(16) > 1.645|H0: ? = 61,000)
= P(Z > 1.645 - 61000 - 60,000/1550/sqrt(16)) = P(Z > -0.935) = 0.1748
c) n = [(Z? + Z?)?/?0]^2
= [1.645+ 1.282)1550/1000]^2
= 20.58 ? 21
So 21 times should be tested.

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