Question

Given the following information:

n = 200 | x = 155

Determine the 95% confidence interval estimate for the population proportion.

Answer 1

Solution :

Given that,

n = 200

x = 155

Point estimate = sample proportion = = x / n = 155 / 200 = 0.775

1 - = 1 - 0.775 = 0.225

At 95% confidence level the z 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 * (((0.775 * 0.225) / 200)

= 0.058

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.775 - 0.058 < p < 0.775 + 0.058

0.717 < p < 0.833

The 95% confidence interval for the population proportion p is : (0.717 , 0.833)