Question

according to the centers of disease control, about 21% 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 21%. which are the appropriate null and alternative hypotheses for this study? (h_0: p = 21%, h_a: p
eq21%) (h_0: p
eq0, h_a: p = 0) (h_0: p = 21%, h_a: p>21%) (h_0: p = 21%, h_a: p<21%) suppose that the result is to reject (h_0). which is the proper conclusion? there is not sufficient evidence to support the claim that the students at his local schools have a smaller proportion of obese students. 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.

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 21% or 0.21. The student claims that the proportion of obese students in local schools is less than 21%. So, $H_0$ should be the statement that the proportion is equal to the national average and $H_A$ should be the statement that the proportion is less than the national average.
$H_0: p = 0.21$, $H_A: p<0.21$ (where $p$ is the proportion of obese students in local schools).

Step2: Interpret the result of rejecting $H_0$

When we reject the null hypothesis ($H_0$), we have sufficient evidence in favor of the alternative hypothesis ($H_A$). Since $H_A$ is that the proportion of obese students in local schools is less than 21%, rejecting $H_0$ means there is sufficient evidence to support the claim that the students at his local schools have a smaller proportion of obese students.

Answer:

1. $H_0: p = 21\%$, $H_A: p<21\%$
2. There is sufficient evidence to support the claim that the students at his local schools have a smaller proportion of obese students.