Question

Express the confidence interval

Answer 1

Answer:

$\hat p = \frac{0.244+0.326}{2}=0.285$

$ME = \frac{0.326-0.244}{2}=0.041$

$0.285 \pm 0.041$

Step-by-step explanation:

For this case we have a confidence interval given as a percent:

$24.4\% \leq p \leq 32.6\%$

If we express this in terms of fraction we have this:

$0.244 \leq p \leq 0.326$

We know that the confidence interval for the true proportion is given by:

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

And thats equivalent to:

$\hat p \pm ME$

We can estimate the estimated proportion like this:

$\hat p = \frac{0.244+0.326}{2}=0.285$

And the margin of error can be estimaed using the fact that the confidence interval is symmetrical

$ME = \frac{0.326-0.244}{2}=0.041$

And then the confidence interval in the form desired is:

$0.285 \pm 0.041$