High School

An automobile manufacturer claims that its jeep has a 35.5 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 220 jeeps, they found a mean MPG of 35.9. Assume the standard deviation is known to be 2.2. A level of significance of 0.02 will be used.

Make a decision to reject or fail to reject the null hypothesis.

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.

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