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Question 671:



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If we used the z-test, the test-statistic z* is found as the difference between the sample mean and test mean = 508-500 = 8 divided by the standard error of the difference (SE).

SE is the standard deviation divided by the square root of the sample size = 30.2/SQRT(49) = 4.314. This would make the test statistic = 8/4.314 = 1.854.  We lookup the p-value in a normal table for 2-sided area for the value of 1.854 and get .06369 (or use the percentile to z-score calculator).  Since this is above the alpha of .01 we would NOT reject the NULL hypothesis and cannot conclude the mean is different than 500.

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