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.

Step-by-step explanation:

Since we have given that

p = 0.34

x= 228

n = 750

So, $\hat{p}=\dfrac{x}{n}=\dfrac{228}{750}=0.304$

So, hypothesis would be

$H_0:p=\hat{p}\\\\H_a:p\neq \hat{p}$

So, test statistic value would be

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.304-0.38}{\sqrt{\dfrac{0.38\times 0.62}{750}}}\\\\z=\dfrac{-0.076}{0.0177}\\\\z=-4.293$

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.