Question

when we select a random sample of 100 young women in your community, we find that 20% are infected with at least one of the most common stds. which gives the best interpretation of the 95% confidence interval to estimate the percentage of young women in your community who are infected with at least one of the most common stds?

Answer 1

We are 95% certain that 12 to 28% of the young women in your neighborhood have at least one of the most prevalent STDS.

This is further explained below.

What is the required interpretation?

Generally, Given that the parameters are

n=100

P=0.20

at $\alpha=0.05\left(0 .5 \quad \tau_{\alpha / 2}=1.96\right.$

95% C. I

The equation for the confidence interval is

$P \pm z \sqrt{\frac{p(1-p)}{n}}$

Where

n=sample size

P=sample proportion

Hence solve for the confidence interval

0.20$\pm$ 1.96 $\sqrt{\frac{0.20(1-0.20)}{100}}$

0.20 $\pm$ 0.0784

$(0.1216,0.2784)$

(12%, 28%)

Interpretation: We have a 95% confidence that between 12 and 28 percent of the young women in your area are infected with at least one of the most frequent STDs.

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