4. In a recent publication, it was reported that the average highway gas mileage of tested models of a new car was 34.2mpg with a standard deviation of 1.5 mpg, with the mileages approximately normally distributed.

H0 : = 34.2

Ha : < 34.2

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 = 0.05?

Part c: If the actual population average gas mileage is 33.8 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.