Question

Construct a​ 95% confidence interval to estimate the population proportion using the data below.    

x equals 27

n equals 75

N equals 500

The​ 95% confidence interval for the population proportion is (____,____)

Answer 1

Solution :

Here n , nq hat > 10

Given that,

Point estimate = sample proportion = = x / n = 27 / 75 = 0.36

Z_/2 = 1.96

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

= 1.96 * (((0.36 * 0.64) / 75)

= 0.109

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.36 - 0.109 < p < 0.36 + 0.109

0.251 < p < 0.469

(0.251 , 0.469)