An automobile manufacturer claims that its carsaverage more than 410 miles per tankful (mpt).
As evidence, they cite an experiment in which 17 cars were drivenfor one tankful each and
averaged 420 mpt. Assume ? = 14 is known.
a. Is the claim valid? Test at the 5 percent level ofsignificance.
b. How high could they have claimed the mpt to be? That is, basedon this experiment, what is the maximum value for µ which wouldhave been rejected as an hypothesized value?
c. What is the power of the test in part (a) when the true value ofµ is 420 mpt? (Hint: Your rejection region for part (a) was statedin terms of comparing Zobs with a cut-off point on the Zdistribution. Find the corresponding x?cut-off and restate yourrejection region in
terms of comparing the observed x?value with thex?cut-off. Then assume H1 is true (i.e. µ
= 420 mpt) and find the probability that x?is in the rejectionregion.)
