A manufacturer of a certain type of tires claims that their tire lifetime is 30,000 miles....

A manufacturer of a certain type of tires claims that their tire lifetime is 30,000 miles. The Bureau of Consumer Protection wants to conduct an preliminary investigation on this claim.

a. If the true lifetime is only 29,000 miles, what is the chance that the Bureau won’t be able to detect such difference with data only on 16 tires? Assume that the SD of all tire lifetimes is about 1,500 miles.

b. How many tires should the Bureau test on so that they can detect the lifetime of 29,000 miles or less with 90% power?

Expert Solution

Let us assume that level of significance is 0.05.

(a)

Here we need to find the power of the test.

Answer: 0.7611

(b)

Answer: 20

orchestra answered 2 years ago

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