Question

In an exit poll, for which the sample size is 2797, the sampling distribution of the sample proportion voting for the incumbent has mean 0.554. Find a 95% confidence interval (z*=1.96) to determine the proportion of all voters who will vote for the incumbent.

(If you know how to calculate using ZInterval on the TI-84, that would also be very helpful-- Thank you!)

Answer 1

Solution :

Given that,

n = 2797

= 0.554

1 - = 1 - 0.554 = 0.446

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 * (((0.554 * 0.446) / 2797)

= 0.018

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.554 - 0.018 < p < 0.554 + 0.018

0.536 < p < 0.572

(0.536, 0.572)