The height of adults living in a suburban area of a large ci

The height of adults living in a suburban area of a large city has a mean equal to 67 inches with a standard deviation of 2.18 inches. In a sample of 178 adults living in the inner-city area, the mean height is found to be 65 inches. Assume that the standard deviation is the same for the two groups.
(a) State the appropriate null and alternative hypothesis to test if the mean heights are significantly different. Use a two-sided hypothesis test.
(b) Using = 0.05, would you reject H0?
(c) Report the p-value for this test. In your own words, what is the meaning of this p-value?
(d) Suppose the mean for the inner-city group is known to be 66.5 inches. Find the power of the test.

Solution