Question

In 2008, the Centers for Disease Control and Prevention reported that 34% of adults in the United States are obese. A country health service planning a new awareness campaign polls a random sample of 750 adults living there. In this sample, 228 people were found to be obese based on their answers to a health questionnaire. Do these response provide strong evidence that the 34% figure is not accurate for this region?

Answer 1

Answer: No, these response does not provide strong evidence that the 34% figure is not accurate for this region.

Explanation:

Since we have given that

p = 0.34

x= 228

n = 750

So,
`\hat{p}=(x)/(n)=(228)/(750)=0.304`

So, hypothesis would be

`H_0:p=\hat{p}\\\\H_a:p\\eq \hat{p}`

So, test statistic value would be

`z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}\\\\z=\frac{0.304-0.38}{\sqrt{(0.38* 0.62)/(750)}}\\\\z=(-0.076)/(0.0177)\\\\z=-4.293`

At 95% confidence , z = 1.96

So, 1.96>-4.293.

So, we accept the null hypothesis.

No, these response does not provide strong evidence that the 34% figure is not accurate for this region.