Middle School

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A study of 4,430 U.S. adults found that 2,913 were obese or overweight.

The 95% confidence interval for the proportion of adults in the U.S. who are obese or overweight is:

A. (0.646, 0.669)
B. (0.644, 0.672)
C. (0.639, 0.676)
D. (0.650, 0.665)

Answer :

Answer:

[tex]0.658 - 1.96\sqrt{\frac{0.658(1-0.658)}{4430}}=0.644[/tex]

[tex]0.658 + 1.96\sqrt{\frac{0.658(1-0.658)}{4430}}=0.672[/tex]

We ar confident that the true proportion of people in US who are obes is between 0.644 and 0.672

And the best option is given by:

(0.644, 0.672)

Step-by-step explanation:

For this case we can begin calculating the proportion of people overweight with this formula:

[tex]\hat p =\frac{2913}{4430}= 0.658[/tex]

The confidence level is 95% , and the significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]

The confidence interval for the mean is given by the following formula:

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

Replacing the info given we got:

[tex]0.658 - 1.96\sqrt{\frac{0.658(1-0.658)}{4430}}=0.644[/tex]

[tex]0.658 + 1.96\sqrt{\frac{0.658(1-0.658)}{4430}}=0.672[/tex]

We ar confident that the true proportion of people in US who are obes is between 0.644 and 0.672

And the best option is given by:

(0.644, 0.672)

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