Answer:
[tex]\hat p = \frac{0.244+0.326}{2}=0.285[/tex]
[tex] ME = \frac{0.326-0.244}{2}=0.041[/tex]
[tex] 0.285 \pm 0.041[/tex]
Step-by-step explanation:
For this case we have a confidence interval given as a percent:
[tex] 24.4\% \leq p \leq 32.6\%[/tex]
If we express this in terms of fraction we have this:
[tex] 0.244 \leq p \leq 0.326 [/tex]
We know that the confidence interval for the true proportion is given by:
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
And thats equivalent to:
[tex]\hat p \pm ME[/tex]
We can estimate the estimated proportion like this:
[tex]\hat p = \frac{0.244+0.326}{2}=0.285[/tex]
And the margin of error can be estimaed using the fact that the confidence interval is symmetrical
[tex] ME = \frac{0.326-0.244}{2}=0.041[/tex]
And then the confidence interval in the form desired is:
[tex] 0.285 \pm 0.041[/tex]
