A car manufacturer claims that its vehicles average at least 28 miles per gallon. Suppose, in fact, the cars only get 26.5 miles per gallon on average, with a population variance of 1. For an appropriate hypothesis test at a .975 confidence level, what is the power of a test of the company’s claim using a sample size of 4 cars?
a. .1492 b. .4658 c. .6543 d. .8508 e. .9236
Suppose amongst all the families on a Caribbean Cruise, the population variance of the number of children per family is 4. If we were to take a sample of 10 families, then the probability is .9 that the sample variance is less than ___. (Hint: Use the χ2 distribution.)
a. 6.53 b. 9.45 c. 14.7 d. 16.2 e. 17.8