Question

The Congressional Budget Office reports that 36% of federal civilian employees have a bachelor's degree or higher (The Wall Street Journal). A random sample of 122 employees in the private sector showed that 34 have a bachelor's degree or higher. Does this indicate that the percentage of employees holding bachelor's degrees or higher in the private sector is less than in the federal civilian sector? Use α = 0.05.

Answer 1

Given that population proportion po = 0.36 and sample proportion p(hat) = 34/122 = 0.28, sample size is n = 122

Null hypothesis Ho: p = 0.36

Alternate hypothesis Ha: p<0.36

z test statistics =

using z table, check -1.8 in the left column and 0.04 in the top row, then select the intersecting cell, we get

p value = 0.0329

p value is less than significance level 0.05, rejecting the null hypothesis.

So, result indicate that the percentage of employees holding bachelor's degrees or higher in the private sector is less than in the federal civilian sector