Question

in a random sample of 36 employees 28 employees answered yes to the question do you earn paid vacation? Use the +4 method in the table below to find a 90% confidence interval for the true proportion of employees who are unpaid vacation

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

Sample size = n = 36

Number of employees with unpaid vacation = x = 36 - 28 = 8

P = x/n = 8/36 = 0.22222

Confidence level = 90%

Critical Z value = 1.6449

(by using z-table)

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

Confidence Interval = 0.22222 ± 1.6449* sqrt(0.22222*(1 – 0.22222)/ 36)

Confidence Interval = 0.22222 ± 1.6449*0.0693

Confidence Interval = 0.22222 ± 0.1140

Lower limit = 0.22222 - 0.1140 = 0.1083

Upper limit = 0.22222 + 0.1140 = 0.3362

Confidence interval = (0.1083, 0.3362)