Question

Construct a confidence interval of the population proportion at the given level of confidence.x=120​, n=1100​, 94​% confidence.

The lower bound of the confidence interval is:

(Round to three decimal places as​ needed.)

The upper bound of the confidence interval is:

​(Round to three decimal places as​ needed.)

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 120 / 1100 = 0.109

1 - = 1 - 0.109 = 0.891

Z_/2 = 1.881

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

= 1.881 * (((0.109 * 0.891) / 1100)

Margin of error = E = 0.018

A 94% confidence interval for population proportion p is ,

- E < p < + E

0.109 - 0.018 < p < 0.109 + 0.018

0.091 < p < 0.127

The lower bound is 0.091

The upper bound is 0.127