Practice 18 The US Department of Health and Human Services i

Practice #18

The US Department of Health and Human Services is concerned about increasing obesities among the American adults. The department surveyed the whole US population 10 years ago. As a result, the average male weight was 190 (unit: pound) and the variance of the male weight was 285.

In this year, due to the limitation of budget, the department has selected a random sample of 101 male adults. The sample mean of the male weight is 198 (pounds). The sample variance of the male weight is 368. 2

(a) While assuming no significant change in the average weight of Americans, the department is trying to judge from the sample whether the average American weight has increased over the past decade. Does the sample allow the department to conclude that the average American weight has increased?

(b) Determine whether the P-value (that would be obtained from the hypothesis testing in (a)) is greater or smaller than 0.05. Explain the reason by drawing an appropriate probability density curve.

(c) Carry out a hypothesis testing of whether the population variance in the current year has a different value from that of 10 years ago.

Solution