Question

State the hypothesis and identify the claim, find the critical value(s), compute the test value, make the decision, summarize the results (make the appropriate statement of the results of the claim included rejection or non-rejection of the null hypothesis). Please show all of your work. USE Z VALUE. Please include bell graph.

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.

NO P VALUE!!!

Answer 1

Null hypothesis H0: Proportion of young people of ages 3-19 obese = 0.27 ( Also the claim )

Alternate hypothesis H1: Proportion of young people of ages 3-10 obese $\neq$ 0.27

The test statistic is given by :

2 = p-P Po(1-P) 12 Where - z = Test statistics a n = Sample size ро = Null hypothesized value Ô = Observed proportion

n = 300 , $\widehat{p}$ = 103/300 = 0.34 , p₀ = 0.27, $\alpha = 0.05$

034-027 0.27+ ( 10.27) 300

$z = \frac{0.34-0.27}{\sqrt{\frac{0.27*(1-0.27)}{300}}} = \frac{.07}{0.0256} = 2.734$

Hence, the calculated test statistic is 2.734.

Now, the critical z value at 0.05 level of significance is 1.96

Decision rule : If Z is less than -1.96, or greater than 1.96, reject the null hypothesis otherwise accept null hypothesis.

The bell graph:

Probability 95% 2.5% 2.5%

Now, since our z value is 2.734 which is greater than 1.96, hence, we reject the null hypothesis that Proportion of young people of ages 3-19 obese = 0.27