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 31 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 = 0.05.

Answer 1

There is sufficient evidence to conclude at the 0.05 level of significance that the percentage of employees holding bachelor's degrees or higher in the private sector is less than in the federal civilian sector.

How to solve

State the null and alternate hypotheses:

H₀: The percentage of employees holding bachelor's degrees or higher in the private sector is the same as or greater than in the federal civilian sector.

H₁: The percentage of employees holding bachelor's degrees or higher in the private sector is less than in the federal civilian sector.

Calculate the sample proportion of employees with bachelor's degrees or higher in the private sector:

p = 31/122 = 0.2541

Find the critical value for a two-tailed test with α = 0.05:

z* = -1.96

Calculate the standard error of the proportion:

SE = √(p(1 - p)/n) = √(0.2541(0.7459)/122) ≈ 0.0362

Calculate the test statistic:

z = (p - p₀)/SE = (0.2541 - 0.36)/0.0362 ≈ -2.95

Make a decision about the null hypothesis:

Since z < -z*, we reject the null hypothesis.

Conclusion:

There is sufficient evidence to conclude at the 0.05 level of significance that the percentage of employees holding bachelor's degrees or higher in the private sector is less than in the federal civilian sector.