Question

according to the centers of disease control, about 22% of american young people between the ages of 12 and 19 are obese. a student claims that the students in his local schools are in better shape than the national average, so their proportion of obese students is less than 22%. which are the appropriate null and alternative hypotheses for this study? h0: p = 22%, ha: p ≠ 22% h0: p ≠ 0, ha: p = 0 h0: p = 22%, ha: p > 22% h0: p = 22%, ha: p < 22% suppose that the result is to reject h0. which is the proper conclusion? there is not enough information to answer this question. there is sufficient evidence to support the claim that the students at his local schools have a smaller proportion of obese students. there is not sufficient evidence to support the claim that the students at his local schools have a smaller proportion of obese students.

Explanation:

Step1: Define null and alternative hypotheses

The null hypothesis ($H_0$) is a statement of no - effect or no difference. The alternative hypothesis ($H_A$) is what we are trying to find evidence for. The national proportion of obese students is 22%. The student claims that the proportion of obese students in local schools is less than 22%. So, $H_0$: $p = 22\%$ and $H_A$: $p<22\%$.

Step2: Interpret the rejection of the null hypothesis

When we reject the null hypothesis, it means that we have enough evidence to support the alternative hypothesis. Since $H_A$ is that the proportion of obese students in local schools is less than 22%, rejecting $H_0$ implies that there is sufficient evidence to support the claim that the students at his local schools have a smaller proportion of obese students.

Answer:

1. $H_0$: $p = 22\%$, $H_A$: $p<22\%$
2. There is sufficient evidence to support the claim that the students at his local schools have a smaller proportion of obese students.