Question 672:

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Step 1:  We are given the population standard deviation of 2.5 so we can use the z-test to test the hypothesis. The Null hypothesis is the mean time is 7 minutes or less. The alternative hypothesis is the mean time is greater than 7 minutes.
Ho: :μ<= 7,  Ha: μ > 7

Step 2: The critical value for the z test for an alpha of .02 using a 1-tailed hypothesis test is found from the normal table. The critical value is 2.054.

Step 3:  The test statistic z, is found as the difference between sample and test mean = 1.2 minutes divided by the Standard error of the difference (SE). The SE is the standard deviation divided by the square root of the sample size = 2.5/SQRT(25) = .5. The test statistic is 1.2/.5 = 2.4.

Step 4:  Since the test statistic is greater than the critical value 2.4 > 2.054 we reject the null hypothesis.

Step 5: We conclude there is sufficient evidence at the alpha level of .02 to conclude the  average time to wait is greater than 7 minutes.

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