Question

10. In a poll, 396 out of 825 New York voters surveyed indicated that they approve of the job DeBlasio has done as mayor. Make a 99% confidence interval for the percentage of all New York voters who would approve of DeBlasio’s performance as mayor. Describe the meaning of the interval that you found.

Answer 1

$99\ \% \ CI = \widehat{p} \pm \ 2.58 \sqrt{\widehat{p}(1- \widehat{p}) /n}$

$\widehat{p} = \ \frac{396}{825}= 0.48, n = 825$

On putting the these values in above formula , we get

99% CI = ( 0.48-0.045, 0.48+0.045)

=(0.435 , 0.525)

We are 99% confident with the sample data that the population proportion of voters will fall within that range.