Question

construct a 90% confidence interval

x=2544

n=3814

Answer 1

Solution:

Confidence interval for Population Proportion is given as below:

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Where, P is the sample proportion, Z is critical value, and n is sample size.

We are given

x = 2544

n = 3814

P = x/n = 2544/3814 = 0.667016256

Confidence level = 90%

Critical Z value = 1.6449

(by using z-table)

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Confidence Interval = 0.667016256 ± 1.6449* sqrt(0.667016256*(1 – 0.667016256)/3814)

Confidence Interval = 0.667016256 ± 1.6449* 0.0076

Confidence Interval = 0.667016256 ± 0.0126

Lower limit = 0.667016256 - 0.0126 = 0.6545

Upper limit = 0.667016256 + 0.0126 = 0.6796

Confidence interval = (0.6545, 0.6796)