MS1023 Business Statistics with Computer Applications
Homework #4
MS1023 Business Statistics w/Comp Apps I
Homework #4 – Use Red Par Score Form
Chps. 9 & 10: 50 Questions Only
7. The rejection region for a hypothesis test
becomes smaller if the level of significance
is changed from 0.01 to 0.05.
1. The first step in testing a hypothesis is to
establish a true null hypothesis and a false
alternative hypothesis.
a) True
b) False
a) True
b) False
8. Whenever hypotheses are established
such that the alternative hypothesis is "μ>8",
where μ is the population mean, the
hypothesis test would be a two-tailed test.
2. In testing hypotheses, the researcher
initially assumes that the alternative
hypothesis is true and uses the sample data
to reject it.
a) True
b) False
a) True
b) False
3. The null and the alternative hypotheses
must be mutually exclusive and collectively
exhaustive.
a) True
b) False
4. Generally speaking, the hypotheses that
business researchers want to prove are stated
in the alternative hypothesis.
a) True
b) False
5. When a true null hypothesis is rejected,
the researcher has made a Type I error.
a) True
b) False
6. When a false null hypothesis is rejected,
the researcher has made a Type II error.
a) True
b) False
Maho Sonmez maho.sonmez@utsa.edu
9. Whenever hypotheses are established
such that the alternative hypothesis is "μ >
8", where μ is the population mean, the pvalue is the probability of observing a
sample mean greater than the observed
sample mean assuming that μ ≥ 8.
a) True
b) False
10. If a null hypothesis was not rejected at
the 0.10 level of significance, it will be
rejected at a 0.05 level of significance based
on the same sample results.
a) True
b) False
11. Consider the following null and
alternative hypotheses.
Ho: 67
Ha: > 67
These hypotheses _______________.
a) indicate a one-tailed test with a rejection
area in the right tail
b) indicate a one-tailed test with a rejection
area in the left tail
c) indicate a two-tailed test
d) are established incorrectly
e) are not mutually exclusive
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MS1023 Business Statistics with Computer Applications
Homework #4
12. Consider the following null and
alternative hypotheses.
Ho: p .16
Ha: p < .16
These hypotheses _______________.
a) reject
b) not reject
c) redefine
d) change the alternate hypothesis into
e) restate
a) indicate a one-tailed test with a rejection
area in the right tail
b) indicate a one-tailed test with a rejection
area in the left tail
c) indicate a two-tailed test
d) are established incorrectly
e) are not mutually exclusive
16. A researcher is testing a hypothesis of a
single mean. The critical t value for = .05
and a two-tailed test is +2.0796. The
observed t value from sample data is -2.92.
The decision made by the researcher based
on this information is to _____ the null
hypothesis.
13. Suppose the alternative hypothesis in a
hypothesis test is: "the population mean is
less than 60". If the sample size is 27, is
unknown, and alpha =.05, the critical value
of t is _______.
a) reject
b) not reject
c) redefine
d) change the alternate hypothesis into
e) restate
a) 2.0555
b) -2.0555
c) -1.7056
d) -1.7033
e) -2.0518
17. The diameter of 3.5 inch diskettes is
normally distributed. Periodically, quality
control inspectors at Dallas Diskettes
randomly select a sample of 16 diskettes. If
the mean diameter of the diskettes is too
large or too small the diskette punch is shut
down for adjustment; otherwise, the
punching process continues. The null
hypothesis is ______.
14. Suppose the alternative hypothesis in a
hypothesis test is "the population mean is
greater than 60". If the sample size is 24,
is unknown, and alpha = .01, the critical
value of t is _______.
a) -2.8073
b) -2.7969
c) 2.8073
d) 2.4999
e) 2.4922
15. A researcher is testing a hypothesis of a
single mean. The critical t value for = .05
and a one-tailed test is 2.0639. The observed
t value from sample data is 1.742. The
decision made by the researcher based on
this information is to ______ the null
hypothesis.
Maho Sonmez maho.sonmez@utsa.edu
a) n 16
b) n = 16
c) = 3.5
d) 3.5
e) ≥ 3.5
18. The diameter of 3.5 inch diskettes is
normally distributed. Periodically, quality
control inspectors at Dallas Diskettes
randomly select a sample of 16 diskettes. If
the mean diameter of the diskettes is too
large or too small the diskette punch is shut
down for adjustment; otherwise, the
punching process continues. The last
sample showed a mean and standard
deviation of 3.55 and 0.08 inches,
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MS1023 Business Statistics with Computer Applications
Homework #4
respectively. Using = 0.05, the
appropriate decision is _______.
21. Using = 0.01, the appropriate decision
is to _______ the null hypothesis.
a) reject the null hypothesis and shut down
the punch
b) reject the null hypothesis and do not shut
down the punch
c) do not reject the null hypothesis and shut
down the punch
d) do not reject the null hypothesis and do
not shut down the punch
e) do nothing
a) reject
b) not reject
c) redefine
d) change the alternate hypothesis into
e) restate
The following data (in pounds), which were
selected randomly from a normally
distributed population of values, represent
measurements of a machine part that is
supposed to weigh, on average, 8.3 pounds.
8.1
8.4
8.2
8.5
8.4
8.3
8.3
8.7
8.3
8.4
8.1
8.2
8.2
8.3
8.5
8.8
8.4
8.6
8.2
8.5
Use these data and alpha = 0.01 to test the
hypothesis that the parts average 8.3 pounds.
Answer the questions 19-21 based on the
above information.
19. The null hypothesis is ______.
a) n 20
b) n = 20
c) = 8.3
d) 8.3
e) ≥ 8.3
Downtime in manufacturing is costly and
can result in late deliveries, backlogs, failure
to meet orders, and even loss of market
share. Suppose a manufacturing plant has
been averaging 23 minutes of downtime per
day for the past several years, but during the
past year, there has been a significant effort
by both management and production
workers to reduce downtime. In an effort to
determine if downtime has been
significantly reduced, company productivity
researchers have randomly sampled 31 days
over the past several months from company
records and have recorded the daily
downtimes shown below in minutes. Use
these data and an alpha of .01 to test to
determine if downtime has been
significantly reduced. Assume that daily
downtimes are normally distributed in the
population.
19
16
23
26
23
24
22
18
27
22
19
17
27
28
19
26
19
17
19
15
21
32
24
17
18
16
24
19
18
25
21
20. The critical value is ______.
a) -2.8609
b) 2.8609
c) ±2.8453
d) ±2.5395
e) ±2.8609
Maho Sonmez maho.sonmez@utsa.edu
Answer the questions 22-25 based on the
above information.
22. The alternative hypothesis is ______.
a) = 23
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MS1023 Business Statistics with Computer Applications
b) > 23
c) ≤ 23
d) 23
e) < 23
23. The critical value is ______.
a) -2.4528
b) 2.4528
c) 2.4573
d) -2.4573
e) ±2.7500
24. Using = 0.01, the appropriate decision
is to _______ the null hypothesis
a) reject
b) not reject
c) redefine
d) change the alternate hypothesis into
e) restate
25. Using = 0.05, the appropriate decision
is to _______ the null hypothesis
a) reject
b) not reject
c) redefine
d) change the alternate hypothesis into
e) restate
26. Ophelia O’Brien, VP of Consumer
Credit of American First Banks (AFB),
monitors the default rate on personal loans
at the AFB member banks. One of her
standards is "no more than 5% of personal
loans should be in default." On each Friday,
the default rate is calculated for a sample of
500 personal loans. Last Friday’s sample
contained 30 defaulted loans. The null
hypothesis is _______.
a) p ≥ 0.05
b) p ≤ 0.05
c) p > 0.05
Maho Sonmez maho.sonmez@utsa.edu
Homework #4
d) p < 0.05
e) p = 0.05
27. Ophelia O’Brien, VP of Consumer
Credit of American First Banks (AFB),
monitors the default rate on personal loans
at the AFB member banks. One of her
standards is "no more than 5% of personal
loans should be in default." On each Friday,
the default rate is calculated for a sample of
500 personal loans. Last Friday’s sample
contained 30 defaulted loans. Using =
0.10, the critical z value is _______.
a) 1.645
b) -1.645
c) 1.28
d) -1.28
e) 2.28
28. Ophelia O’Brien, VP of Consumer
Credit of American First Banks (AFB),
monitors the default rate on personal loans
at the AFB member banks. One of her
standards is "no more than 5% of personal
loans should be in default." On each Friday,
the default rate is calculated for a sample of
500 personal loans. Last Friday’s sample
contained 30 defaulted loans. Using =
0.10, the observed z value is _______.
a) 1.03
b) -1.03
c) 0.046
d) -0.046
e) 1.33
29. Ophelia O’Brien, VP of Consumer
Credit of American First Banks (AFB),
monitors the default rate on personal loans
at the AFB member banks. One of her
standards is "no more than 5% of personal
loans should be in default." On each Friday,
the default rate is calculated for a sample of
500 personal loans. Last Friday’s sample
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MS1023 Business Statistics with Computer Applications
contained 30 defaulted loans. Using =
0.10, the appropriate decision is _______.
a) reduce the sample size
b) increase the sample size
c) reject the null hypothesis
d) do not reject the null hypothesis
e) do nothing
30. Ophelia O’Brien, VP of Consumer
Credit of American First Banks (AFB),
monitors the default rate on personal loans
at the AFB member banks. One of her
standards is "no more than 5% of personal
loans should be in default." On each Friday,
the default rate is calculated for a sample of
500 personal loans. Last Friday’s sample
contained 38 defaulted loans. Using =
0.10, the appropriate decision is _______.
a) reduce the sample size
b) increase the sample size
c) reject the null hypothesis
d) do not reject the null hypothesis
e) do nothing
31. The executives of CareFree Insurance,
Inc. feel that "a majority of our employees
perceive a participatory management style at
CareFree." A random sample of 200
CareFree employees is selected to test this
hypothesis at the 0.05 level of significance.
Eighty employees rate the management as
participatory. The null hypothesis is
__________.
a) p ≥ 40
b) p < 40
c) p ≥ 0.50
d) p < 0.50
e) n > 200
32. A study by Hewitt Associates showed
that 79% of companies offer employees
flexible scheduling. Suppose a researcher
believes that in accounting firms this figure
Maho Sonmez maho.sonmez@utsa.edu
Homework #4
is lower. The researcher randomly selects
415 accounting firms and through interviews
determines that 303 of these firms have
flexible scheduling. With a 1% level of
significance, does the test show enough
evidence to conclude that a significantly
lower proportion of accounting firms offer
employees flexible scheduling?
a) Reject the null hypothesis, concluding
that the lower proportion of accounting
firms offer employees flexible scheduling.
b) Do not reject the null hypothesis,
concluding that the lower proportion of
accounting firms offer employees flexible
scheduling.
c) Reject the null hypothesis, concluding
that the higher proportion of accounting
firms offer employees flexible scheduling.
d) Do not reject the null hypothesis,
concluding that the higher proportion of
accounting firms offer employees flexible
scheduling.
e) The test is inconclusive.
Suppose a Realtor is interested in comparing
the asking prices of midrange homes in
Peoria, Illinois, and Evansville, Indiana. The
Realtor conducts a small telephone survey in
the two cities, asking the prices of midrange
homes. A random sample of 21 listings in
Peoria resulted in a sample average price of
$116,900, with a standard deviation of
$2,300. A random sample of 26 listings in
Evansville resulted in a sample average
price of $114,000, with a standard deviation
of $1,750. The Realtor assumes prices of
midrange homes are normally distributed
and the variance in prices in the two cities is
about the same. The researcher wishes to
test whether there is any difference in the
mean prices of midrange homes of the two
cities for alpha = .01.
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MS1023 Business Statistics with Computer Applications
Answer the questions 33-36 based on the
above information.
33. The null hypothesis for this problem is
______.
a) 1 – 2 < 0
b) 1 – 2 > 0
c) 1 – 2 = 1
d) 1 – 2 0
e) 1 – 2 = 0
34. The degrees of freedom for this problem
are _______.
a) 20
b) 25
c) 46
d) 45
e) 43
35. The critical t value from table is ____.
a) ±2.6870
b) ±2.6896
c) ±2.4121
d) ±2.0141
e) ±1.6794
36. The appropriate decision for this
problem is to _____________.
Homework #4
nine car rental companies in Dallas results in
a sample mean of $44 and a standard
deviation of $3. Use alpha = 0.05 to test to
determine whether the average daily car
rental rates in Boston are significantly higher
than those in Dallas. Assume car rental rates
are normally distributed and the population
variances are equal.
Answer the questions 37-40 based on the
above information.
37. The null hypothesis for this problem is
______.
a) 1 – 2 < 0
b) 1 – 2 > 0
c) 1 – 2 = 1
d) 1 – 2 0
e) 1 – 2 = 0
38. The degrees of freedom for this problem
are _______.
a) 7
b) 8
c) 9
d) 15
e) 16
a) not reject the null hypothesis, 1 – 2 = 0
b) reject the null hypothesis, 1 – 2 ≥ 0
c) reject the null hypothesis 1 – 2 = 0
d) not reject the null hypothesis, 1 – 2 ≤ 0
e) reject the null hypothesis 1 – 2 = 1
39. The critical t value from table is ____.
Based on an indication that mean daily car
rental rates may be higher for Boston than
for Dallas, a survey of eight car rental
companies in Boston is taken and the sample
mean car rental rate is $47, with a standard
deviation of $3. Further, suppose a survey of
40. The appropriate decision for this
problem is to _____________.
Maho Sonmez maho.sonmez@utsa.edu
a) -1.7531
b) 1.7531
c) -2.1314
d) 2.1314
e) ±1.6794
a) not reject the null hypothesis, 1 – 2 ≤ 0
b) reject the null hypothesis, 1 – 2 ≥ 0
c) reject the null hypothesis 1 – 2 = 0
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MS1023 Business Statistics with Computer Applications
d) reject the null hypothesis, 1 – 2 ≤ 0
e) not reject the null hypothesis 1 – 2 ≥ 0
41. A researcher wants to conduct a
before/after study on 11 subjects to
determine if a treatment results in any
difference in scores. The null hypothesis is
that the average difference is zero while the
alternative hypothesis is that the average
difference is not zero. Scores are obtained
on the subjects both before and after the
treatment. After subtracting the after scores
from the before scores, the average
difference is computed to be -2.40 with a
sample standard deviation of 1.21. Assume
that the differences are normally distributed
in the population. The degrees of freedom
for this test are _______.
a) 11
b) 2
c) 9
d) 20
e) 10
42. A researcher wants to conduct a
before/after study on 11 subjects to
determine if a treatment results in any
difference in scores. The null hypothesis is
that the average difference is zero while the
alternative hypothesis is that the average
difference is not zero. Scores are obtained
on the subjects both before and after the
treatment. After subtracting the after scores
from the before scores, the average
difference is computed to be -2.40 with a
sample standard deviation of 1.21. Assume
that the differences are normally distributed
in the population. The observed t value for
this test is _______.
a) -6.58
b) -21.82
c) -2.4
d) 1.98
e) 2.33
Maho Sonmez maho.sonmez@utsa.edu
Homework #4
43. A researcher wants to conduct a
before/after study on 11 subjects to
determine if a treatment results in any
difference in scores. The null hypothesis is
that the average difference is zero while the
alternative hypothesis is that the average
difference is not zero. Scores are obtained
on the subjects both before and after the
treatment. After subtracting the after scores
from the before scores, the average
difference is computed to be -2.40 with a
sample standard deviation of 1.21. A 0.05
level of significance is selected. Assume
that the differences are normally distributed
in the population. The table t value for this
test is _______.
a) ±1.8125
b) ±2.2622
c) ±1.7959
d) ±2.2281
e) ±3.1693
One of the new thrusts of quality control
management is to examine the process by
which a product is produced. This approach
also applies to paperwork. In industries
where large long-term projects are
undertaken, days and even weeks may
elapse as a change order makes its way
through a maze of approvals before
receiving final approval. This process can
result in long delays and stretch schedules to
the breaking point. Suppose a quality control
consulting group claims that it can
significantly reduce the number of days
required for such paperwork to receive
approval. In an attempt to “prove” its case,
the group selects five jobs for which it
revises the paperwork system. The following
data show the number of days required for a
change order to be approved before the
group intervened and the number of days
required for a change order to be approved
7
MS1023 Business Statistics with Computer Applications
after the group instituted a new paperwork
system.
Before After
12
8
7
3
10
8
16
9
8
5
Use alpha = 0.05 to determine whether there
was a significant drop in the number of days
required to process paperwork to approve
change orders. Assume that the differences
in days are normally distributed.
Homework #4
47. What is the appropriate critical value for
this problem for alpha = 0.01?
a) 4.6041
b) 4.0321
c) 3.3649
d) 4.5407
e) 3.7469
48. Mean sample difference (̅ ) is _______.
a) 10.6
b) 6.6
c) 4
d) -4
e) 17.2
Answer the questions 44-50 based on the
above information.
49. The observed value of t for this problem
is __________.
44. The null hypothesis for this problem is
_____.
a) 4.78
b) 2.05
c) 4.87
d) -4.78
e) -2.05
a) D = 0
b) D ≥ 0
c) D ≤ 0
d) D ≠ 0
e) D ≥ 1
45. The degrees of freedom in this problem
are _______.
a) 3
b) 8
c) 5
d) 9
e) 4
50. The appropriate conclusion for this
problem is ___________.
a) not reject the null hypothesis, D ≤ 0
b) reject the null hypothesis, D ≥ 0
c) reject the null hypothesis D = 0
d) reject the null hypothesis, D ≤ 0
e) not reject the null hypothesis D ≥ 0
46. The sample standard deviation (sd) of the
differences is _______.
a) 1.6733
b) 1.6373
c) 1.8807
d) 1.8708
e) 1.8078
Maho Sonmez maho.sonmez@utsa.edu
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