Question

If nequals=100 and Xequals=35​, construct a 95​% confidence interval estimate of the population proportion.

Answer 1

Solution :

Given that,

n = 100

x = 35

Point estimate = sample proportion = = x / n = 0.35

1 - = 0.65

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.35 * 0.65) / 100)

= 0.093

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.35 - 0.093 < p < 0.35 + 0.093

0.257 < p < 0.443

The 95% confidence interval for the population proportion p is : (0.257 , 0.443)