Question

Survey results for a sample of 1,863 Americans showed that 71% agreed the process of registering and voting should be made easy so all citizens can vote.

Calculate the 95% Confidence Interval estimate for the population proportion.

Answer 1

Solution :

Given that,

n = 1863

Point estimate = sample proportion = =0.71

1 -   = 1- 0.71 =0.29

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 (((0.71*0.29) / 1863)

E = 0.021

A 95% confidence interval for proportion p is ,

- E < p < + E

0.71-0.021 < p < 0.71+0.021

0.689< p < 0.731