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.**

*H*_{0}: *p* ≥ 0.36;
*H*_{1}: *p* < 0.36

*H*_{0}: *μ* = 0.36;
*H*_{1}: *μ* ≠
0.36

*H*_{0}: *μ* ≥ 0.36;
*H*_{1}: *μ* < 0.36

*H*_{0}: *p* = 0.36;
*H*_{1}: *p* ≠ 0.36

*H*_{0}: *μ* ≤ 0.36;
*H*_{1}: *μ* > 0.36

*H*_{0}: *p* ≤ 0.36;
*H*_{1}: *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**

*H*_{0}: *μ* ≥ 0.36;
*H*_{1}: *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.

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.
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civilian employees have a bachelor's degree or higher (The Wall
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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.
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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 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.
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