Question

The Congressional Budget Office reports that 36% of federal civilian employees have a bachelor's degree or...

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.

Homework Answers

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.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The Congressional Budget Office reports that 36% of federal civilian employees have a bachelor's degree or...
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 115 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. a.) What are we testing in this problem? -single proportion -single...
The Congressional Budget Office reports that 36% of federal civilian employees have a bachelor's degree or...
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 117 employees in the private sector showed that 30 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 are we testing in this problem? single meansingle proportion     What...
The Congressional Budget Office reports that 36% of federal civilian employees have a bachelor's degree or...
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.
The Congressional Budget Office reports that 36% of federal civilian employees have a bachelor's degree or...
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...
A random sample of 36 values is drawn from a mound-shaped and symmetric distribution. The sample...
A random sample of 36 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 8 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 7.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown. No, the x distribution is skewed left.     No, the...
A random sample of 36 values is drawn from a mound-shaped and symmetric distribution. The sample...
A random sample of 36 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 14 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 13.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown.No, the x distribution is skewed left.    No, the x distribution...
A random sample of 36 values is drawn from a mound-shaped and symmetric distribution. The sample...
A random sample of 36 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 9 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 8.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown.No, the x distribution is skewed left.    No, the x distribution...
A random sample of 36 values is drawn from a mound-shaped and symmetric distribution. The sample...
A random sample of 36 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 11 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 10.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown.No, the x distribution is skewed left.     No, the x distribution...
A random sample of 25 values is drawn from a mound-shaped and symmetric distribution. The sample...
A random sample of 25 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 11 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 10.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown. No, the x distribution is skewed left.    No, the...
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample...
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 11 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 10.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown.No, the x distribution is skewed left.    No, the x distribution...