Question

Wi-Fi Access A survey of 50 students in grades 4 through 12 found 68% have classroom Wi-Fi access. Find the 99% confidence interval of the population proportion.

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

n = 50

P = x/n = 0.68

Confidence level = 99%

Critical Z value = 2.5758

(by using z-table)

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

Confidence Interval = 0.68 ±2.5758* sqrt(0.68*(1 – 0.68)/50)

Confidence Interval = 0.68 ± 2.5758*0.0660

Confidence Interval = 0.68 ± 0.1699

Lower limit = 0.68 - 0.1699 = 0.5101

Upper limit = 0.68 + 0.1699 = 0.8499

Confidence interval = (0.5101, 0.8499)