Question

10) A researcher claims that based on the information obtained from CHOC, 27% of young people ages 3-19 are obese. To test this claim, she randomly selected 300 people ages 3-19 and found that 103 were obese. At a = 0.05, is there enough evidence to reject the claim?

Answer 1

Here the researcher claims 27% of young people are obese.As null hypothesis always has an equality sign claim will be null hypothesis.So null and alternate hypothesis are:

$H_0:p=0.27$

$H_a:p\neq0.27$

Now we will find test statistic.

103 = 0.343 300

$z=\frac{\widehat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.343-0.27}{\sqrt{\frac{0.27*0.73}{300}}}=2.848$

P-value for two tailed test forP(z>2.848)=2*0.0022=0.0044

ん 0

As P-value(0.0044) is less than alpha(0.05) we reject the null hypothesis.

So we do not have enough evidence(at significance level 0.05) to support the claim that 27% of young people ages 3-19 are obese.