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 123 employees in the private sector showed that 32 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.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c) Find (or estimate) the P-value.

P-value > 0.250

0.125 < P-value < 0.250

0.050 < P-value < 0.125

0.025 < P-value < 0.050

0.005 < P-value < 0.025

P-value < 0.005

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.36

H_a : p < 0.36

n = 123

x = 32

= x / n = 32 / 123 = 0.2602

P₀ = 0.36

1 - P₀ = 1 - 0.36 = 0.64

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.2602 - 0.36 / [(0.36 * 0.64) / 123]

= -2.307

Test statistic = -2.31

P(z < -2.31) = 0.0104

P-value = 0.0104

0.005 < P-value < 0.025

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to the percentage of employees holding bachelor's degrees or higher

in the private sector is less than in the federal civilian sector .