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

H_{0} : p = 0.36

H_{a} : p < 0.36

n = 123

x = 32

= x / n = 32 / 123 = 0.2602

P_{0} = 0.36

1 - P_{0} = 1 - 0.36 = 0.64

z = - P_{0} / [P_{0 *} (1 -
P_{0} ) / 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 .

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 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 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...

A study is made of residents in Phoenix and its suburbs
concerning the proportion of residents who subscribe to Sporting
News. A random sample of n1 = 90 urban residents showed that r1 =
10 subscribed, and a random sample of n2 = 99 suburban residents
showed that r2 = 18 subscribed. Does this indicate that a higher
proportion of suburban residents subscribe to Sporting News? Use a
5% level of significance. What are we testing in this problem?
single...

Each box of Healthy Crunch breakfast cereal contains a coupon
entitling you to a free package of garden seeds. At the Healthy
Crunch home office, they use the weight of incoming mail to
determine how many of their employees are to be assigned to
collecting coupons and mailing out seed packages on a given day.
(Healthy Crunch has a policy of answering all its mail on the day
it is received.) Let x = weight of incoming mail and
y...

The Nero Match Company sells matchboxes that are supposed to
have an average of 40 matches per box, with σ = 8. A
random sample of 96 matchboxes shows the average number of matches
per box to be 42.5. Using a 1% level of significance, can you say
that the average number of matches per box is more than 40?
What are we testing in this problem?
A.) single mean
B.) single
proportion
(a) What is the level of significance?...

In this problem, assume that the distribution of differences is
approximately normal. Note: For degrees of freedom d.f. not in the
Student's t table, use the closest d.f. that is smaller. In some
situations, this choice of d.f. may increase the P-value by a small
amount and therefore produce a slightly more "conservative"
answer.
In environmental studies, sex ratios are of great importance.
Wolf society, packs, and ecology have been studied extensively at
different locations in the U.S. and foreign...

In this problem, assume that the distribution of differences is
approximately normal. Note: For degrees of freedom d.f. not in the
Student's t table, use the closest d.f. that is smaller. In some
situations, this choice of d.f. may increase the P-value by a small
amount and therefore produce a slightly more "conservative" answer.
In environmental studies, sex ratios are of great importance. Wolf
society, packs, and ecology have been studied extensively at
different locations in the U.S. and foreign...

In this problem, assume that the distribution of differences is
approximately normal. Note: For degrees of freedom
d.f. not in the Student's t table, use
the closest d.f. that is smaller. In
some situations, this choice of d.f. may increase
the P-value by a small amount and therefore produce a
slightly more "conservative" answer.
In environmental studies, sex ratios are of great importance. Wolf
society, packs, and ecology have been studied extensively at
different locations in the U.S. and foreign...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 34 minutes ago

asked 41 minutes ago

asked 51 minutes ago

asked 54 minutes ago

asked 54 minutes ago

asked 56 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago