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

Solution :

a)

Type II error is the probability of fail to reject false null hypothesis.

That is resercher incorrectly conclude that mileage is 33.2 mpg while actually it is less than 33.2 mpg.

b)

Sample mean less than equal to 32.79 mpg will lead to rejection of H0.

c)

Type II error is 0.516

d)

As the sample size increases power of test will also increase. So the type II error will decrease..