Answer :
Final answer:
To decide on the null hypothesis concerning the fuel economy of jeeps, a Z-test would be used given the sample mean, known standard deviation, and sample size. The null hypothesis would be rejected if the p-value is less than the level of significance, 0.02.
Explanation:
The question involves evaluating whether to reject or fail to reject the null hypothesis in a one-sample hypothesis test concerning fuel economy (MPG) of jeeps.
With a sample mean MPG of 35.9, a known standard deviation of 2.2, and a sample size of 220 jeeps, we need to use the Z-test for a known population standard deviation to decide on the hypothesis. Since the level of significance is 0.02, we can compare the calculated p-value to this alpha value to make our decision.
To perform the test, we would calculate the Z-score using the formula: Z = (sample mean - population mean) / (standard deviation / sqrt(sample size)).
In our case, if the calculated p-value is less than 0.02, we would reject the null hypothesis, indicating that the actual MPG is significantly different from the manufacturer's claim. If the p-value is greater than 0.02, we would fail to reject the null hypothesis, implying that there isn't enough evidence to dispute the manufacturer's MPG rating claim.