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 32have 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.

a. What are we testing in this problem?

single mean

single proportion     

b. What is the level of significance?


c. State the null and alternate hypotheses.

H₀: p ≥ 0.36; H₁:  p < 0.36

H₀: μ = 0.36; H₁: μ ≠ 0.36     

H₀: μ ≥ 0.36; H₁:  μ < 0.36

H₀: p = 0.36; H₁:  p ≠ 0.36

H₀: μ ≤ 0.36; H₁: μ > 0.36

H₀: p ≤ 0.36; H₁: p > 0.36

d. What sampling distribution will you use?

The standard normal.

The Student's t.     

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


f. 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

g. Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.     

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

h. Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that the proportion of bachelor or higher degrees in the private sector is less than in the federal civilian sector.

There is insufficient evidence at the 0.05 level to conclude that the proportion of bachelor or higher degrees in the private sector is less than in the federal civilian sector.

Answer 1

a)

single proportion  

level of significance =0.05

H₀: μ ≥ 0.36; H₁:  μ < 0.36

d)

The standard normal since np >=5 and nq >=5

e)

sample success x   =		32
sample size          n    =		123
std error   se =√(p*(1-p)/n) =		0.0433
sample proportion p̂ = x/n=		0.2602
test stat z =(p̂-p)/√(p(1-p)/n)=		-2.31

f)

0.005 < P-value < 0.025

g)At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

h)

There is sufficient evidence at the 0.05 level to conclude that the proportion of bachelor or higher degrees in the private sector is less than in the federal civilian sector.