A physical anthropologist studying the effects of nutritional changes on human morphometrics is interested in the impact of Western diet on the heights of adult Japanese males. Studies prior to World War II indicated that the heights of adult Japanese males had a mean of 64.0 inches and a standard deviation of 2.0 inches. The anthropologist measured the heights of a random sample of 25 adult Japanese men and found their height to average 66.5 inches with a standard deviation of 3.0 inches.

(a) Calculate the 95% confidence interval for mean from the sample. (b) Calculate the 95% confidence interval for variance from the sample. (c) Has the mean height changed since World War II? Write out the hypotheses associated with this question and perform the test. (d) Has the variance of heights changed since World War II? Again, write out the hypothesis associated with this question and perfrom the test. (e)Has the variance of heights changes since world war 2? again write out the hypothesis associated with this question and perform the test.