Question

(1 point) A poll of ? n voters is to be taken in an attempt to predict the outcome of a by-election in a certain riding. Specifically, you are interested in the proportion of voters that will vote for a certain candidate, Candidate A. ?=440 n = 440 voters have been randomly chosen, each has indicated what candidate they will vote for. You are to count the number, out of 440, who say they will vote for Candidate A. This count is measured by the random variable ? X . You find ?=185 X = 185 . (a) Find a 97% confidence interval for ? p , the proportion of all voters who will vote for Candidate A. Use at least four decimal points for your lower and upper bounds. Lower Bound = = equation editorEquation Editor Upper Bound = = equation editorEquation Editor

Answer 1

Solution :

Given that,

n = 440

x = 185

Point estimate = sample proportion = = x / n = 185 / 440 = 0.4205

1 - = 1 - 0.4205 = 0.5795

At 97% confidence level the z is ,

= 1 - 97% = 1 - 0.97 = 0.03

/ 2 = 0.03 / 2 = 0.015

Z_/2 = Z _0.015 = 2.17

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

= 2.17 * (((0.4205 * 0.5795) / 440)

= 0.0511

A 97% confidence interval for population proportion p is ,

- E < p < + E

0.4205 - 0.0511 < p < 0.4205 + 0.0511

0.3694 < p < 0.4716

Lower bound = 0.3694

Upper bound = 0.4716