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 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 is the level of significance?

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

What sampling distribution will you use?

The Student's *t*.The standard
normal.

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

Estimate the *P*-value.

*P*-value > 0.2500.125 < *P*-value <
0.250 0.050 < *P*-value <
0.1250.025 < *P*-value < 0.0500.005 <
*P*-value < 0.025*P*-value < 0.005

Sketch the sampling distribution and show the area corresponding to
the *P*-value.

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.

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

The statistical software output for this problem is :

Single proportion

(a)

Level of significance = 0.05

Option **A** is correct.

(b)

The standard normal.

Test statistics = -2.33

(c)

0.005 < *P*-value < 0.025

(d)

Option **A** is correct.

(e)

Option **A** is correct.

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 ...

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 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.
What is the value of the sample test statistic? (Round your...

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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
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(a) Is it appropriate to use a Student's t
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Yes, because the x distribution is mound-shaped and
symmetric and σ is unknown.No, the x distribution
is skewed left. No, the x
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symmetric distribution. The sample mean is 11 and the sample
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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 16 values is drawn from a mound-shaped and
symmetric distribution. The sample mean is 13 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
12.5.
(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 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
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