Question

Calculate a 90% confidence interval for the true proportion:
True: 20
False: 8
Total: 28

Answer 1

Solution :

Given that,

n = 238

x = 20

= x / n = 20 / 28 = 0.714

1 - = 1 - 0.714 = 0.286

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (((0.714 * 0.286) / 28)

= 0.140

A 90% confidence interval for population proportion p is ,

- E < P < + E

0.714 - 0.140 < p < 0.714 + 0.140

0.574 < p < 0.854

(0.574 , 0.854)