The U.S. Office of Personnel Management reports that 51% of
federal civilian employees have a bachelor's degree or higher
(OPM.gov). A random sample of 106 employees in the private
sector showed that 44 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
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: p = 0.51; H1: p > 0.51H0: p = 0.51; H1: p < 0.51 H0: μ = 0.51; H1: μ > 0.51H0: μ = 0.51; H1: μ ≠ 0.51H0: μ = 0.51; H1: μ < 0.51H0: p = 0.51; H1: p ≠ 0.51
(b) What sampling distribution will you use? What assumptions are
you making?
The Student's t, since np < 5 and nq < 5.The Student's t, since np > 5 and nq > 5. The standard normal, since np < 5 and nq < 5.The standard normal, since np > 5 and nq > 5.
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 > 0.2500.125 < P-value < 0.250 0.050 < P-value < 0.1250.020 < P-value < 0.0500.005 < P-value < 0.020P-value < 0.005
Sketch the sampling distribution and show the area corresponding to
the P-value.
![]() |
![]() |
![]() |
![]() |
(d) Based on your answers in parts (a) to (c), 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.
(e) Interpret your conclusion in the context of the
application.
There is sufficient evidence at the 0.05 level to conclude that the proportion of employees holding bachelor's degrees or higher 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 employees holding bachelor's degrees or higher in the private sector is less than in the federal civilian sector.
The statistic software output for this problem is:
Level of significance = 0.05
H0 : p = 0.51
HA : p < 0.51
The standard normal, since np > 5 and nq > 5.
Test statistics = -1.95
0.020 < P-value < 0.05
(d)
Option a)
(e)
Option a)
The U.S. Office of Personnel Management reports that 51% of federal civilian employees have a bachelor's...
The Congressional budget Office reports that 36% of federal civilian employees have a bachelor's degree or higher (The Wall Street Journa). A random sample of 115 employees in the private sector showed that I 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 avan sector? Use a 0.05. What are we testing in this problem? Single proportion single mean (a)...
Professor Jennings claims that only 35% of the students at Flora
College work while attending school. Dean Renata thinks that the
professor has underestimated the number of students with part-time
or full-time jobs. A random sample of 85 students shows that 40
have jobs. Do the data indicate that more than 35% of the students
have jobs? Use a 5% level of significance.
What are we testing in this problem?
single meansingle proportion
(a) What is the level of significance?...
Women athletes at the a certain university have a long-term
graduation rate of 67%. Over the past several years, a random
sample of 36 women athletes at the school showed that 22 eventually
graduated. Does this indicate that the population proportion of
women athletes who graduate from the university is now less than
67%? Use a 5% level of significance.
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: p = 0.67;
H1: p <...
A hospital reported that the normal death rate for patients with
extensive burns (more than 40% of skin area) has been significantly
reduced by the use of new fluid plasma compresses. Before the new
treatment, the mortality rate for extensive burn patients was about
60%. Using the new compresses, the hospital found that only 44 of
93 patients with extensive burns died. Use a 1% level of
significance to test the claim that the mortality rate has
dropped.
What are...
Women athletes at the a certain university have a long-term
graduation rate of 67%. Over the past several years, a random
sample of 37 women athletes at the school showed that 23 eventually
graduated. Does this indicate that the population proportion of
women athletes who graduate from the university is now less than
67%? Use a 10% level of significance.
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: p = 0.67;
H1: p >...
A random sample of 40 binomial trials resulted in 16 successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05. (a) Can a normal distribution be used for the p̂ distribution? Explain. Yes, np and nq are both less than 5.No, np is greater than 5, but nq is less than 5. No, nq is greater than 5, but np is less than 5.Yes, np and nq are both greater...
Symposium is part of a larger work referred to as
Plato's Dialogues. Wishart and Leach† found that about
21.4% of five-syllable sequences in Symposium are of the
type in which four are short and one is long. Suppose an
antiquities store in Athens has a very old manuscript that the
owner claims is part of Plato's Dialogues. A random sample
of 484 five-syllable sequences from this manuscript showed that 128
were of the type four short and one long. Do...
What is your favorite color? A large survey of countries,
including the United States, China, Russia, France, Turkey, Kenya,
and others, indicated that most people prefer the color blue. In
fact, about 24% of the population claim blue as their favorite
color.† Suppose a random sample of n = 54 college students
were surveyed and r = 10 of them said that blue is their
favorite color. Does this information imply that the color
preference of all college students is...
Recall that Benford's Law claims that numbers chosen from very
large data files tend to have "1" as the first nonzero digit
disproportionately often. In fact, research has shown that if you
randomly draw a number from a very large data file, the probability
of getting a number with "1" as the leading digit is about 0.301.
Now suppose you are an auditor for a very large corporation. The
revenue report involves millions of numbers in a large computer
file....
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 15 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 14.5. (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...