Question

Construct a confidence interval of the population proportion at the given level of confidence. x equals=120​, n equals=1200​, 99​% confidence

Answer 1

Solution :

Given that,

n = 1200

x = 120

Point estimate = sample proportion = = x / n = 120 / 1200 = 0.100

1 - = 0.900

Z_/2 = 2.576

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

= 2.576 * (((0.100 * 0.900) / 1200)

= 0.022

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.100 - 0.022 < p < 0.100 + 0.022

0.078 < p < 0.122

The 99% confidence interval for the population proportion p is : (0.078 , 0.122)