Currently an automaker provides a warranty that covers all new cars for 24,000 m

Question

Currently an automaker provides a warranty that covers all new cars for 24,000 miles. The quality-assurance department suggests that the mean number of miles driven by the owners of the new cars exceeds 24,000. The automaker would like to revise and possibly increase its automobile warranty policy. A random sample of 35 car owners surveyed and the sample mean number of miles driven is calculated as x^bar = 24, 421 with the sample standard deviation of s = 1, 944 miles. a. Using a 5% significance level, conduct the following test of hypothesis: {H_0: mu lessthanorequalto 24,000 H_a > 24,000 b. Find the largest value of the sample mean for which the null hypothesis is not rejected c. Suppose the true population mean is 25,000 miles. What is the probability that this change is not detected?

Explanation / Answer

a) TS = (Xbar - mu)/(s/sqrt(n))

=(24421 -24000)/(1944/sqrt(35))

= 1.2812

t-distribution with df= n-1= 34

critical value = 1.691

since TS < critical value , we fail to reject the null

b) largest value = 24000 + 1.691* 1944/sqrt(35) =24555.655

c) P(Xbar < 24555.655 | mu = 25000)

= P(t <(24555.655 -25000)/(1944/sqrt(35)))

=P(t< -1.35225)

=0.0926

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