Question

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.
(d) Has the variance of heights changed since World War II? Again, write out the hypothesis associated
with this question.
(e) Relate the confidence intervals in (a) and (b) to the hypotheses in (c) and (d).

Answer 1

Given information:

(a)

Degree of freedom: df=n-1=24

The critical value of t, using excel function "=TINV(0.05,24)", for 95% confidence interval is 2.064.

The confidence interval is;

(b)

Degree of freedom df=n-1=25-1=24 and for 95% confidence interval value critical value of chi sqaure statitics will be

The confidence interval for the population variance is

(c)

Hypotheses are:

(d)

Hypotheses are:

(e)

Since confidence interval of part a does not contain 64 so null hypothesis of part c is rejected.

Since confidence interval of part b does not contain 4 so null hypothesis of part d is rejected.