Question

Ms. Maria is considering running for mayor for Bear Gulch.  Before completing the petitions, she conducted a survey of voters in Bear Gulch. A sample of 500 voters reveals 400 would support her in the upcoming election.

a. Estimate the value of the population proportion.

b. What is the 95% confidence interval?

Answer 1

Solution :

Given that,

n = 500

x = 400

Point estimate = sample proportion = = x / n = 400/500=0.8

1 -   = 1-0.8 =0.2

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   ( Using z table )

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

= 1.96 (((0.8*0.2) / 500)

E = 0.0351

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.8-0.0351 < p < 0.8+0.0351

0.7649< p < 0.8351

The 95% confidence interval for the population proportion p is : 0.7649, 0.8351