Question

An automobile manufacturer has given its jeep a 30.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 110 jeeps, they found a mean MPG of 30.5 . Assume the population variance is known to be 3.61 . Is there sufficient evidence at the 0.05 level to support the testing firm's claim?

Step 1: state the null & alternative hypothesis

Step 2 : Find the value of the test statistic. Round your answer to two decimal places.

Step 3: specify if it is a one or two tailed

step 4: find the p value of the test statistic

step 5: identify the level of significance of the hypothesis test

step 6: reject or fail to reject the hypothesis Please circle answers so I can follow steps properly

Answer 1

Given: = 30.7, = 30.5, s = 1.9, n = 110, = 0.05

(1) The Hypothesis:

H0: = 30.7

Ha: 30.7

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(2) The Test Statistic: Since the population standard deviation is known, we use the z test.

The test statistic is given by the equation:

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(3) This is a 2 tailed test

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(4) The p Value:    The p value (2 Tail) for Z = -1.1,is; p value = 0.1907

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(5) The level of significance, = 0.05

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(6) The Decision Rule:   If P value is < , Then Reject H0.

The Decision: Since P value (0.1907) is > (0.05) , We Fail to Reject H0.

The Conclusion: There isn't sufficient evidence at the 95% significance level to warrant rejection of the automobile manufacturers claim that the average mileage of its Jeep is equal to 30.7 miles/gallon.

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