Question

A recent poll of 450 college-age students found that 270 agreed with U.S. foreign policy toward Israel. What is the corresponding 80% confidence interval?

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 = 270

n = 450

P = x/n = 270/450 = 0.6

Confidence level = 80%

Critical Z value = 1.2816

(by using z-table)

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

Confidence Interval = 0.6 ± 1.2816* sqrt(0.6*(1 – 0.6)/450)

Confidence Interval = 0.6 ± 1.2816*0.0231

Confidence Interval = 0.6 ± 0.0296

Lower limit = 0.6 - 0.0296 = 0.5704

Upper limit = 0.6 + 0.0296 = 0.6296

Confidence interval = (0.5704, 0.6296)