Question

4. In a recent publication, it was reported that the average highway gas mileage of tested models of a new car was 33.2 mpg with a standard deviation of 2.5 mpg, with the mileages approximately normally distributed.

H0 : µ = 33.2

Ha : µ < 33.2

Part a: Describe a Type II error in the context of the hypothesis test.

Part b: If a simple random sample of 100 cars is selected, what values of the sample mean ¯x would represent sufficient evidence to reject the null hypothesis at significance level α = 0.05?

Part c: If the actual population average gas mileage is 32.8 mpg, determine the probability that the null hypothesis will be rejected if a simple random sample of 100 cars is selected.

Part d: If the sample size were greater than 100 cars, what would happen to the probability in Part c? Explain your reasoning.

Answer 1