CHAPTER 12: INFERENCE ABOUT A POPULATION
TRUE/FALSE
1. In order to determine the p-value associated with hypothesis testing about the
population mean µ, it is necessary to know the value of the test statistic.
ANS: T PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
2. In order to interpret the p-value associated with hypothesis testing about the popula-
tion mean µ, it is necessary to know the value of the test statistic.
ANS: F PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
3. If a sample has 15 observations and a 95% confidence estimate for µ is needed, the
appropriate value of t is 1.753.
ANS: F PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
4. If a sample has 18 observations and a 90% confidence estimate for µ is needed, the
appropriate value of t is 1.740.
ANS: T PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
5. The statistic when the sampled population is normal is Student t-distributed with n
degrees of freedom.
ANS: F PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Knowledge
6. If the sampled population is nonnormal, the t-test of the population mean µ is still
valid, provided that the condition is not extreme.
ANS: T PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
7. A race car driver tested his car for time from 0 to 60 mph, and in 20 tests obtained an
average of 48.5 seconds with a standard deviation of 1.47 seconds. A 95% confidence interval for the 0
to 60 time is 45.2 seconds to 51.8 seconds.
ANS: F PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
, 8. In forming a 95% confidence interval for a population mean from a sample size of 20,
the number of degrees of freedom from the t-distribution equals 20.
ANS: F PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
9. The t-distribution is used in a confidence interval for a mean when the actual standard
error is not known.
ANS: T PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
10. The t-distribution allows the calculation of confidence intervals for means for small
samples when the population variance is not known, regardless of the shape of the distribution in the
population.
ANS: F PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
11. The t-distribution is used to develop a confidence interval estimate of the population
mean when the population standard deviation is unknown.
ANS: T PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Knowledge
12. The t-distribution assumes that the population is normally distributed.
ANS: T PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
13. In estimating the population mean with the population standard deviation unknown, if
the sample size is 16, there are 8 degrees of freedom.
ANS: F PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
MULTIPLE CHOICE
1. For statistical inference about the mean of a single population when the population
standard deviation is unknown, the degrees for freedom for the t-distribution equal n − 1 because we
lose one degree of freedom by using the:
a. sample mean as an estimate of the population mean.
b. sample standard deviation as an estimate of the population standard deviation.
c. sample proportion as an estimate of the population proportion.
d. sample size as an estimate of the population size.
ANS: A PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
,KEY: Bloom's: Comprehension
2. Researchers determined that 60 Puffs tissues is the average number of tissues used
during a cold. Suppose a random sample of 100 Puffs users yielded the following data on the number
of tissues used during a cold: = 52 and s = 22. Suppose the test statistic does not fall in the rejection
region at α = 0.05. Which of the following conclusions is correct?
a. At α = 0.05, we do not reject H0. c. At α = 0.05, we accept H0.
b. At α = 0.05, we reject H0. d. Both a and c.
ANS: A PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
3. A robust estimator is one that is:
a. unbiased and symmetrical about zero. c. efficient and less spread out.
b. consistent and is also mound-shaped. d. not sensitive to moderate nonnormality.
ANS: D PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
4. A random sample of size 15 taken from a normally distributed population revealed a
sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the
population mean would equal:
a. 77.77 c. 88.85
b. 72.23 d. 77.27
ANS: A PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
5. A major electronics store chain is interested in estimating the average amount its credit
card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts
were randomly sampled and analyzed with the following results: = $50.50 and s2 = 400. A 95%
confidence interval for the average amount the credit card customers spent on their first visit to the
chain's new store in the mall is:
a. $50.50 ± $9.09. c. $50.50 ± $11.08.
b. $50.50 ± $10.12. d. None of these choices.
ANS: C PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
6. Researchers determine that 60 Puffs tissues is the average number of tissues used
during a cold. Suppose a random sample of 100 Puffs users yielded the following data on the number
of tissues used during a cold: = 52 and s = 22. Using the sample information provided, the value of the
test statistic is:
a. t = (52 − 60) / 22 c. t = (52 − 60) / ()
b. t = (52 − 60) / () d. t = (52 − 60) / ()
ANS: D PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
, 7. For a 99% confidence interval of the population mean based on a sample of n = 25
with s = 0.05, the critical value of t is:
a. 2.7969 c. 2.4922
b. 2.7874 d. 2.4851
ANS: A PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
8. Based on sample data, the 90% confidence interval limits for the population mean are
LCL = 170.86 and UCL = 195.42. If the 10% level of significance were used in testing the hypotheses
H0: µ = 201 vs. H1: µ ≠ 201, the null hypothesis:
a. would be rejected. c. would fail to be rejected.
b. would be accepted. d. would become H0: µ ≠ 201
ANS: A PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
9. The degrees of freedom for the test statistic for µ when σ is unknown is:
a. 1 c. n−1
b. n d. None of these choices.
ANS: C PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
10. Researchers determined that 60 Puffs tissues is the average number of tissues used
during a cold. Suppose a random sample of 100 Puffs users yielded the following data on the number
of tissues used during a cold: = 52 and s = 22. Suppose the alternative we wanted to test was H1: µ <
60. The correct rejection region for α = 0.05 is:
a. reject H0 if t > 1.6604. c. reject H0 if t > 1.9842 or Z < −1.9842.
b. reject H0 if t < −1.6604. d. reject H0 if t < −1.9842.
ANS: B PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
COMPLETION
1. When the population standard deviation is and the popula-
tion is normal, the test statistic for testing hypotheses about µ is the t-distribution with n − 1 degrees of
freedom.
ANS: unknown
PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Knowledge
2. When the population standard deviation is unknown and the population is
, the test statistic for testing hypotheses about µ is the t-distribution with n − 1
degrees of freedom.
TRUE/FALSE
1. In order to determine the p-value associated with hypothesis testing about the
population mean µ, it is necessary to know the value of the test statistic.
ANS: T PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
2. In order to interpret the p-value associated with hypothesis testing about the popula-
tion mean µ, it is necessary to know the value of the test statistic.
ANS: F PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
3. If a sample has 15 observations and a 95% confidence estimate for µ is needed, the
appropriate value of t is 1.753.
ANS: F PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
4. If a sample has 18 observations and a 90% confidence estimate for µ is needed, the
appropriate value of t is 1.740.
ANS: T PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
5. The statistic when the sampled population is normal is Student t-distributed with n
degrees of freedom.
ANS: F PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Knowledge
6. If the sampled population is nonnormal, the t-test of the population mean µ is still
valid, provided that the condition is not extreme.
ANS: T PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
7. A race car driver tested his car for time from 0 to 60 mph, and in 20 tests obtained an
average of 48.5 seconds with a standard deviation of 1.47 seconds. A 95% confidence interval for the 0
to 60 time is 45.2 seconds to 51.8 seconds.
ANS: F PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
, 8. In forming a 95% confidence interval for a population mean from a sample size of 20,
the number of degrees of freedom from the t-distribution equals 20.
ANS: F PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
9. The t-distribution is used in a confidence interval for a mean when the actual standard
error is not known.
ANS: T PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
10. The t-distribution allows the calculation of confidence intervals for means for small
samples when the population variance is not known, regardless of the shape of the distribution in the
population.
ANS: F PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
11. The t-distribution is used to develop a confidence interval estimate of the population
mean when the population standard deviation is unknown.
ANS: T PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Knowledge
12. The t-distribution assumes that the population is normally distributed.
ANS: T PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
13. In estimating the population mean with the population standard deviation unknown, if
the sample size is 16, there are 8 degrees of freedom.
ANS: F PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
MULTIPLE CHOICE
1. For statistical inference about the mean of a single population when the population
standard deviation is unknown, the degrees for freedom for the t-distribution equal n − 1 because we
lose one degree of freedom by using the:
a. sample mean as an estimate of the population mean.
b. sample standard deviation as an estimate of the population standard deviation.
c. sample proportion as an estimate of the population proportion.
d. sample size as an estimate of the population size.
ANS: A PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
,KEY: Bloom's: Comprehension
2. Researchers determined that 60 Puffs tissues is the average number of tissues used
during a cold. Suppose a random sample of 100 Puffs users yielded the following data on the number
of tissues used during a cold: = 52 and s = 22. Suppose the test statistic does not fall in the rejection
region at α = 0.05. Which of the following conclusions is correct?
a. At α = 0.05, we do not reject H0. c. At α = 0.05, we accept H0.
b. At α = 0.05, we reject H0. d. Both a and c.
ANS: A PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
3. A robust estimator is one that is:
a. unbiased and symmetrical about zero. c. efficient and less spread out.
b. consistent and is also mound-shaped. d. not sensitive to moderate nonnormality.
ANS: D PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
4. A random sample of size 15 taken from a normally distributed population revealed a
sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the
population mean would equal:
a. 77.77 c. 88.85
b. 72.23 d. 77.27
ANS: A PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
5. A major electronics store chain is interested in estimating the average amount its credit
card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts
were randomly sampled and analyzed with the following results: = $50.50 and s2 = 400. A 95%
confidence interval for the average amount the credit card customers spent on their first visit to the
chain's new store in the mall is:
a. $50.50 ± $9.09. c. $50.50 ± $11.08.
b. $50.50 ± $10.12. d. None of these choices.
ANS: C PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
6. Researchers determine that 60 Puffs tissues is the average number of tissues used
during a cold. Suppose a random sample of 100 Puffs users yielded the following data on the number
of tissues used during a cold: = 52 and s = 22. Using the sample information provided, the value of the
test statistic is:
a. t = (52 − 60) / 22 c. t = (52 − 60) / ()
b. t = (52 − 60) / () d. t = (52 − 60) / ()
ANS: D PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
, 7. For a 99% confidence interval of the population mean based on a sample of n = 25
with s = 0.05, the critical value of t is:
a. 2.7969 c. 2.4922
b. 2.7874 d. 2.4851
ANS: A PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
8. Based on sample data, the 90% confidence interval limits for the population mean are
LCL = 170.86 and UCL = 195.42. If the 10% level of significance were used in testing the hypotheses
H0: µ = 201 vs. H1: µ ≠ 201, the null hypothesis:
a. would be rejected. c. would fail to be rejected.
b. would be accepted. d. would become H0: µ ≠ 201
ANS: A PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
9. The degrees of freedom for the test statistic for µ when σ is unknown is:
a. 1 c. n−1
b. n d. None of these choices.
ANS: C PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Comprehension
10. Researchers determined that 60 Puffs tissues is the average number of tissues used
during a cold. Suppose a random sample of 100 Puffs users yielded the following data on the number
of tissues used during a cold: = 52 and s = 22. Suppose the alternative we wanted to test was H1: µ <
60. The correct rejection region for α = 0.05 is:
a. reject H0 if t > 1.6604. c. reject H0 if t > 1.9842 or Z < −1.9842.
b. reject H0 if t < −1.6604. d. reject H0 if t < −1.9842.
ANS: B PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Application
COMPLETION
1. When the population standard deviation is and the popula-
tion is normal, the test statistic for testing hypotheses about µ is the t-distribution with n − 1 degrees of
freedom.
ANS: unknown
PTS: 1 DIF: Easy OBJ: SFME.KELL.15.12.01
NAT: BUSPROG.SFME.KELL.15.03 STA: DISC.SFME.KELL.15.06
KEY: Bloom's: Knowledge
2. When the population standard deviation is unknown and the population is
, the test statistic for testing hypotheses about µ is the t-distribution with n − 1
degrees of freedom.
