Question

Construct a 99​% confidence interval to estimate the population proportion with a sample proportion equal to 0.35 and a sample size equal to 120. round to three decimlae places as needed.

Answer 1

Solution :

Given that,

n = 120

= 0.35

1 - = 1 - 0.35 = 0.65

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576* ([(0.35 * 0.65)] / 120)

= 0.112

A 99% confidence interval for population proportion p is ,

- E < P < + E

0.35 - 0.112 < p < 0.35 + 0.112

0.238 < p < 0.462

(0.238, 0.462)