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ms1023_hw3.pdf
MS1023 Business Statistics with Computer Applications Homework #3
Maho Sonmez [email protected] 1
MS1023 Business Statistics w/Comp Apps I
Homework #3 – Use Red Par Score Form
Chp. 7: Questions 1-50
1. Kristen Ashford purchased the subscribers
list for Wind Surfing magazine. She plans
to survey a sample of the subscribers before
using the list in her mail order business. She
chooses the first 100 of the 5,000 names.
Her sample is a _________.
a) simple random sample
b) stratified sample
c) systematic sample
d) convenience sample
e) cluster sample
2. Kristen Ashford purchased the subscribers
list for Wind Surfing magazine. She plans
to survey a sample of the subscribers before
using the list in her mail order business. She
randomly selects the fourth name as a
starting point and then selects every 50th
subsequent name (54, 104, 154, etc.). Her
sample is a _________.
a) simple random sample
b) stratified sample
c) systematic sample
d) convenience sample
e) cluster sample
3. Kristen Ashford purchased the subscribers
list for Wind Surfing magazine. She plans
to survey a sample of the subscribers before
using the list in her mail order business. The
names are numbered consecutively from 1 to
5,000. Kristen chooses her sample by
selecting four-digit numbers (1 to 5,000)
from a random number table. Her sample is
a _________.
a) simple random sample
b) stratified sample
c) systematic sample
d) convenience sample
e) cluster sample
4. A carload of palletized aluminum castings
has arrived at Mansfield Motor
Manufacturers. The car contains 1,000
pallets of 100 castings each. Mario Munoz,
manager of Quality Assurance, directs the
receiving crew to deliver the 127th and
869th pallets to his crew for 100%
inspection. Mario randomly selected 127
and 869 from a table of random numbers.
Mario's sample of 200 castings is a
_____________.
a) simple random sample
b) systematic sample
c) stratified sample
d) cluster sample
e) convenience sample
5. Abel Alonzo, Director of Human
Resources, is exploring employee
absenteeism at the Harrison Haulers Plant.
Abel knows that absenteeism varies
significantly between departments. For
example, workers in the wood shop are
absent more than those in the tuning
department and the size of the departments
ranges from 40 to 120 workers. He orders a
random sample of 10 workers from each of
the six departments. Abel's sample is a
________________.
a) proportionate systematic sample
b) proportionate stratified sample
c) disproportionate systematic sample
d) disproportionate stratified sample
e) proportionate cluster sample
MS1023 Business Statistics with Computer Applications Homework #3
Maho Sonmez [email protected] 2
6. Abel Alonzo, Director of Human
Resources, is exploring employee
absenteeism at the Harrison Haulers Plant.
Abel knows that absenteeism varies
significantly between departments. For
example, workers in the wood shop are
absent more than those in the tuning
department and the size of the departments
ranges from 40 to 120 workers. He orders a
random sample of 10% of the workers from
each of the six departments. Abel's sample
is a ________________.
a) proportionate systematic sample
b) proportionate stratified sample
c) disproportionate systematic sample
d) disproportionate stratified sample
e) proportionate cluster sample
7. Catherine Chao, Director of Marketing
Research, needs a sample of households to
participate in the testing of a new toothpaste
package. She chooses thirty-six of her
closest friends. Catherine's sample is a
_____________.
a) cluster sample
b) convenience sample
c) quota sample
d) systematic sample
e) random sample
8. Catherine Chao, Director of Marketing
Research, needs a sample of households to
participate in the testing of a new toothpaste
package. She directs the seven members of
her staff to find five households each.
Catherine's sample is a _____________.
a) cluster sample
b) proportionate stratified sample
c) quota sample
d) disproportionate stratified sample
e) simple random sample
9. According to the central limit theorem, if
a sample of size 100 is drawn from a
population with a mean of 80, the mean of
all sample means would equal _______.
a) 0.80
b) 8
c) 80
d) 100
e) 120
10. According to the central limit theorem, if
a sample of size 64 is drawn from a
population with a mean of 56, the mean of
all sample means would equal _______.
a) 7.00
b) 56.00
c) 64.00
d) 0.875
e) 128.00
11. According to the central limit theorem, if
a sample of size 100 is drawn from a
population with a standard deviation of 80,
the standard deviation of sample means
would equal _______.
a) 0.80
b) 8
c) 80
d) 800
e) 0.080
12. According to the central limit theorem, if
a sample of size 64 is drawn from a
population with a standard deviation of 80,
the standard deviation of sample means
would equal _______.
a) 10.000
b) 1.250
c) 0.125
d) 0.800
e) 0.080
MS1023 Business Statistics with Computer Applications Homework #3
Maho Sonmez [email protected] 3
13. Increasing the sample size causes the
sampling distribution of x to ________.
a) shift to the right
b) shift to the left
c) have more dispersion
d) have less dispersion
e) stay unchanged
14. According to the central limit theorem,
for samples of size 64 drawn from a
population with = 800 and = 56, the
mean of the sampling distribution of sample
means would equal _______.
a) 7
b) 8
c) 100
d) 800
e) 80
15. According to the central limit theorem,
for samples of size 64 drawn from a
population with = 800 and = 56, the
standard deviation of the sampling
distribution of sample means would equal
_______.
a) 7
b) 8
c) 100
d) 800
e) 80
16. Suppose a population has a mean of 90
and a standard deviation of 28. If a random
sample of size 49 is drawn from the
population, the probability of drawing a
sample with a mean of more than 95 is
_______.
a) 0.1056
b) 0.3944
c) 0.4286
d) 0.8944
e) 1.0000
17. Suppose a population has a mean of 90
and a standard deviation of 28. If a random
sample of size 49 is drawn from the
population, the probability of drawing a
sample with a mean of less than 84 is
_______.
a) 0.9332
b) 0.0668
c) 0.4332
d) 0.8664
e) 1.0000
18. Suppose a population has a mean of 90
and a standard deviation of 28. If a random
sample of size 49 is drawn from the
population, the probability of drawing a
sample with a mean between 85 and 95 is
_______.
a) 0.1056
b) 0.3944
c) 0.7888
d) 0.2112
e) 0.5000
19. Suppose a population has a mean of 90
and a standard deviation of 28. If a random
sample of size 49 is drawn from the
population, the probability of drawing a
sample with a mean between 80 and 100 is
_______.
a) 0.9876
b) 0.0124
c) 0.4938
d) 0.0062
e) 1.0000
MS1023 Business Statistics with Computer Applications Homework #3
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20. Suppose a population has a mean of 450
and a variance of 900. If a random sample of
size 100 is drawn from the population, the
probability that the sample mean is between
448 and 453 is _______.
a) 0.4972
b) 0.6826
c) 0.4101
d) 0.5899
e) 0.9878
21. Suppose a population has a mean of 870
and a variance of 1,600. If a random sample
of size 64 is drawn from the population, the
probability that the sample mean is between
860 and 875 is _______.
a) 0.9544
b) 0.6826
c) 0.8785
d) 0.5899
e) 0.8185
22. Albert Abbasi, VP of Operations at
Ingleside International Bank, is evaluating
the service level provided to walk-in
customers. Accordingly, he plans a sample
of waiting times for walk-in customers. If
the population of waiting times has a mean
of 15 minutes and a standard deviation of 4
minutes, the probability that Albert's sample
of 64 will have a mean less than 14 minutes
is ________.
a) 0.4772
b) 0.0228
c) 0.9772
d) 0.9544
e) 1.0000
23. Albert Abbasi, VP of Operations at
Ingleside International Bank, is evaluating
the service level provided to walk-in
customers. Accordingly, he plans a sample
of waiting times for walk-in customers. If
the population of waiting times has a mean
of 15 minutes and a standard deviation of 4
minutes, the probability that Albert's sample
of 64 will have a mean less than 16 minutes
is ________.
a) 0.4772
b) 0.0228
c) 0.9072
d) 0.9544
e) 0.9772
24. Albert Abbasi, VP of Operations at
Ingleside International Bank, is evaluating
the service level provided to walk-in
customers. Accordingly, he plans a sample
of waiting times for walk-in customers. If
the population of waiting times has a mean
of 15 minutes and a standard deviation of 4
minutes, the probability that Albert's sample
of 64 will have a mean less than 15 minutes
is ________.
a) 0.5000
b) 0.0228
c) 0.9072
d) 0.9544
e) 1.0000
25. Albert Abbasi, VP of Operations at
Ingleside International Bank, is evaluating
the service level provided to walk-in
customers. Accordingly, he plans a sample
of waiting times for walk-in customers. If
the population of waiting times has a mean
of 15 minutes and a standard deviation of 4
minutes, the probability that Albert's sample
of 64 will have a mean between 13.5 and
16.5 minutes is ________.
MS1023 Business Statistics with Computer Applications Homework #3
Maho Sonmez [email protected] 5
a) 0.9974
b) 0.4987
c) 0.9772
d) 0.4772
e) 0.5000
26. Suppose 40% of the population possess a
given characteristic. If a random sample of
size 300 is drawn from the population, then
the probability that 44% or fewer of the
samples possess the characteristic is
_______.
a) 0.0793
b) 0.4207
c) 0.9207
d) 0.9900
e) 1.0000
27. Suppose 30% of a population possess a
given characteristic. If a random sample of
size 1200 is drawn from the population, then
the probability that less than 348 possess
that characteristic is _______.
a) 0.2236
b) 0.2764
c) 0.2900
d) 0.7764
e) 0.3336
28. If the population proportion is 0.90 and a
sample of size 64 is taken, what is the
probability that the sample proportion is less
than 0.88?
a) 0.2019
b) 0.2981
c) 0.5300
d) 0.7019
e) 0.7899
29. If the population proportion is 0.90 and a
sample of size 64 is taken, what is the
probability that the sample proportion is
more than 0.89?
a) 0.1064
b) 0.2700
c) 0.3936
d) 0.6064
e) 0.9000
30. Suppose 40% of all college students
have a computer at home and a sample of 64
is taken. What is the probability that more
than 30 of those in the sample have a
computer at home?
a) 0.3686
b) 0.1314
c) 0.8686
d) 0.6314
e) 0.1343
31. Suppose 40% of all college students
have a computer at home and a sample of
100 is taken. What is the probability that
more than 50 of those in the sample have a
computer at home?
a) 0.4793
b) 0.9793
c) 0.0207
d) 0.5207
e) 0.6754
32. In an instant lottery, your chance of
winning is 0.1. If you play the lottery 100
times and outcomes are independent, the
probability that you win at least 15 percent
of the time is
a) 0.4933
b) 0.5000
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c) 0.1500
d) 0.0478
e) 0.9213
33. Suppose 40% of all college students
have a computer at home and a sample of
100 students is taken. The mean of the
sampling distribution of p is
a) 0.4
b) 0.04
c) 40
d) 0.004
e) 4
34. Suppose 40% of all college students
have a computer at home and a sample of
100 is taken. The standard deviation of the
sampling distribution of p is
a) 4.89
b) 0.0489
c) 0.24
d) 24
e) 0.4
35. If a company employs 3,500 people and
if a random sample of 175 of these
employees has been taken by systematic
sampling, what is the value of k?
a) 3500
b) 175
c) 200
d) 5
e) 20
36. If a company employs 3,500 people and
if a random sample of 175 of these
employees has been taken by systematic
sampling, the researcher would start the
sample selection between what two values?
a) 175 and 3500
b) 0 and 175
c) 0 and 20
d) 0 and 3500
e) 20 and 175
37. A random sample of size 81 is drawn
from a population with a standard deviation
of 12. If only 18% of the time a sample
mean greater than 300 is obtained, what is
the mean of the population?
a) 298.77
b) 301.23
c) 289.77
d) 278.97
e) 277.98
38. Suppose a population proportion is .40,
and 80% of the time when you draw a
random sample from this population you get
a sample proportion of .35 or more. How
large a sample were you taking?
a) 60
b) 86
c) 76
d) 67
e) 68
A Travel Weekly International Air
Transport Association survey asked business
travelers about the purpose for their most
recent business trip. Nineteen percent
responded that it was for an internal
company visit. Suppose 950 business
travelers are randomly selected.
Answer questions 39-41 based on the above
information.
39. What is the probability that more than
25% of the business travelers say that the
MS1023 Business Statistics with Computer Applications Homework #3
Maho Sonmez [email protected] 7
reason for their most recent business trip
was an internal company visit?
a) 0.9999
b) 0.0000
c) 1.0000
d) 0.0100
e) 0.1000
40. What is the probability that between
15% and 20% of the business travelers say
that the reason for their most recent business
trip was an internal company visit?
a) 0.4992
b) 0.1140
c) 0.2852
d) 0.7844
e) 0.7852
41. What is the probability that between 133
and 171 of the business travelers say that the
reason for their most recent business trip
was an internal company visit?
a) 0.49997
b) 0.21477
c) 0.2852
d) 0.78517
e) 0.7852
Suppose the average client charge per hour
for out-of-court work by lawyers in the state
of Iowa is $125. Suppose further that a
random telephone sample of 32 lawyers in
Iowa is taken and that the sample average
charge per hour for out-of-court work is
$110.
Answer the questions 42-45 based on the
above information.
42. If the population variance is $525, what
is the probability of getting a sample mean
of $110 or larger?
a) 0.2500
b) 0.5000
c) 1.0000
d) 0.7500
e) 0.9500
43. If the population variance is $525, what
is the probability of getting a sample mean
larger than $135 per hour?
a) 0.4932
b) 0.5000
c) 0.9932
d) 0.0068
e) 0.5068
44. If the population variance is $525, what
is the probability of getting a sample mean
of between $120 and $130 per hour?
a) 0.3907
b) 0.8907
c) 0.0000
d) 0.1093
e) 0.7814
Questions 45-50 are based on the below
information.
The Aluminum Association reports that the
average American uses 56.8 pounds of
aluminum in a year. A random sample of 51
households is monitored for one year to
determine aluminum usage. If the population
standard deviation of annual usage is 12.3
pounds, what is the probability that the
sample mean will be in each of the
following?
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45. More than 59 pounds _________.
a) 0.1003
b) 0.3997
c) 0.6003
d) 0.8997
e) 0.0003
46. More than 54 pounds _________.
a) 0.4484
b) 0.9484
c) 0.0516
d) 0.8968
e) 0.5516
47. Between 56 and 58 pounds ________.
a) 0.1772
b) 0.2580
c) 0.0808
d) 0.4352
e) 0.5648
48. Less than 55 pounds ________.
a) 0.3531
b) 0.6469
c) 0.8531
d) 0.0668
e) 0.1469
49. Less than 51 pounds ________.
a) 0.4996
b) 0.5004
c) 0.0004
d) 0.9996
e) 0.9992
50. Between 52 and 53 pounds ________.
a) 0.4974
b) 0.0110
c) 0.4864
d) 0.9838
e) 0.0162
Chp. 8: Questions 51-100.
51. Catherine Chao, Director of Marketing
Research, is evaluating consumer
acceptance of a new toothpaste package.
Her staff reports that 17% of a random
sample of 200 households prefers the new
package to all other package designs. If
Catherine concludes that 17% of all
households prefer the new package, she is
using _______.
a) a point estimate
b) a range estimate
c) a statistical parameter
d) an interval estimate
e) an exact estimate
52. Brian Vanecek, VP of Operations at
Portland Trust Bank, is evaluating the
service level provided to walk-in customers.
Accordingly, his staff recorded the waiting
times for 45 randomly selected walk-in
customers, and calculated that their mean
waiting time was 15 minutes. If Brian
concludes that the average waiting time for
all walk-in customers is 15 minutes, he is
using a ________.
a) a range estimate
b) a statistical parameter
c) an interval estimate
d) a point estimate
e) an exact estimate
53. The z value associated with a two-sided
90% confidence interval is _______.
a) 1.28
b) 1.645
c) 1.96
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d) 2.575
e) 2.33
54. The z value associated with a two-sided
95% confidence interval is _______.
a) 1.28
b) 1.645
c) 1.96
d) 2.575
e) 2.33
55. The z value associated with a two-sided
80% confidence interval is _______.
a) 1.645
b) 1.28
c) 0.84
d) 0.29
e) 2.00
56. The z value associated with a two-sided
88% confidence interval is _______.
a) 1.28
b) 1.55
c) 1.17
d) 0.88
e) 1.90
57. The z value associated with a two-sided
99% confidence interval is _______.
a) 1.28
b) 1.645
c) 1.96
d) 2.575
e) 2.33
58. Suppose a random sample of 36 is
selected from a population with a standard
deviation of 12. If the sample mean is 98,
the 99% confidence interval to estimate the
population mean is _______.
a) 94.08 to 101.92
b) 92.85 to 103.15
c) 97.35 to 98.65
d) 93.34 to 102.66
e) 90.20 to 105.00
59. Brian Vanecek, VP of Operations at
Portland Trust Bank, is evaluating the
service level provided to walk-in customers.
Accordingly, his staff recorded the waiting
times for 64 randomly selected walk-in
customers and determined that their mean
waiting time was 15 minutes. Assume that
the population standard deviation is 4
minutes. The 95% confidence interval for
the population mean of waiting times is
________.
a) 14.02 to 15.98
b) 7.16 to 22.84
c) 14.06 to 15.94
d) 8.42 to 21.58
e) 19.80 to 23.65
60. James Desreumaux, VP of Human
Resources of American First Banks (AFB),
is reviewing the employee training programs
of AFB banks. His staff randomly selected
personnel files for 100 tellers in the
Southeast Region and determined that their
mean training time was 25 hours. Assume
that the population standard deviation is 5
hours. The 92% confidence interval for the
population mean of training times is
________.
a) 16.250 to 33.750
b) 24.300 to 25.710
c) 17.950 to 32.050
d) 24.125 to 25.875
e) 24.450 to 27.320
61. The table t value associated with the
upper 5% of the t distribution and 12
degrees of freedom is _______.
a) 2.1788
b) 1.7823
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c) 1.3562
d) 3.0545
e) 1.7959
62. The table t value associated with the
upper 2.5% of the t distribution and 26
degrees of freedom is _______.
a) 1.7056
b) 2.0518
c) 2.7787
d) 2.0555
e) 1.7033
63. The table t value associated with the
upper 10% of the t distribution and 23
degrees of freedom is _______.
a) 1.3195
b) 1.7139
c) 2.4999
d) 1.3178
e) 1.7109
64. A researcher is interested in estimating
the mean value for a population. She takes a
random sample of 17 items and computes a
sample mean of 224 and a sample standard
deviation of 32. She decides to construct a
98% confidence interval to estimate the
mean. The degrees of freedom associated
with this problem are _______.
a) 18
b) 17
c) 16
d) 15
e) 20
65. A researcher is interested in estimating
the mean value for a population. She takes a
random sample of 17 items and computes a
sample mean of 224 and a sample standard
deviation of 32. She decides to construct a
98% confidence interval to estimate the
mean. The table t value associated with this
problem is _______.
a) 2.1199
b) 1.7459
c) 3.6862
d) 2.5669
e) 2.5835
66. A researcher is interested in estimating
the mean value for a population. She takes a
random sample of 17 items and computes a
sample mean of 224 and a sample standard
deviation of 32. She decides to construct a
98% confidence interval to estimate the
mean. The interval is _______.
a) 204.08 to 243.92
b) 203.5 to 244.5
c) 203.332 to 244.668
d) 203.95 to 244.05
e) 204.07 to 245.04
67. Life tests performed on a sample of 13
batteries of a new model indicated: (1) an
average life of 75 months, and (2) a standard
deviation of 5 months. Other battery
models, produced by similar processes, have
normally distributed life spans. The 98%
confidence interval for the population mean
life of the new model is _________.
a) 63.37 to 86.63
b) 61.60 to 88.41
c) 71.77 to 78.23
d) 71.28 to 78.72
e) 79.86 to 81.28
68. A researcher wants to estimate the
proportion of the population which
possesses a given characteristic. A random
sample of size 800 is taken resulting in 360
items which possess the characteristic. The
point estimate for this population proportion
is _______.
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a) 0.55
b) 0.45
c) 0.35
d) 0.65
e) 0.70
69. A random sample of 225 items from a
population results in 60% possessing a given
characteristic. Using this information, the
researcher constructs a 99% confidence
interval to estimate the population
proportion. The resulting confidence interval
is _______.
a) 0.54 to 0.66
b) 0.59 to 0.61
c) 0.57 to 0.63
d) 0.52 to 0.68
e) 0.68 to 0.76
70. Elwin Osbourne, CIO at GFS, Inc., is
studying employee use of GFS e-mail for
non-business communications. A random
sample of 200 e-mail messages was
selected. Thirty of the messages were not
business related. The point estimate for this
population proportion is _______.
a) 0.150
b) 0.300
c) 0.182
d) 0.667
e) 0.786
71. Elwin Osbourne, CIO at GFS, Inc., is
studying employee use of GFS e-mail for
non-business communications. A random
sample of 200 e-mail messages was
selected. Thirty of the messages were not
business related. The 90% confidence
interval for the population proportion is
_________.
a) 0.10847 to 0.19153
b) 0.15300 to 0.24700
c) 0.09126 to 0.20874
d) 0.14521 to 0.25514
e) 0.25514 to 0.26521
72. Elwin Osbourne, CIO at GFS, Inc., is
studying employee use of GFS e-mail for
non-business communications. A random
sample of 200 e-mail messages was
selected. Thirty of the messages were not
business related. The 95% confidence
interval for the population proportion is
_________.
a) 0.10847 to 0.19153
b) 0.15300 to 0.24700
c) 0.09126 to 0.20874
d) 0.10051 to 0.19949
e) 0.19921 to 0.20101
73. Elwin Osbourne, CIO at GFS, Inc., is
studying employee use of GFS e-mail for
non-business communications. A random
sample of 200 e-mail messages was
selected. Thirty of the messages were not
business related. The 98% confidence
interval for the population proportion is
_________.
a) 0.10847 to 0.19153
b) 0.15300 to 0.24700
c) 0.09126 to 0.20874
d) 0.14521 to 0.25514
e) 0.25514 to 0.26521
74. A researcher wants to determine the
sample size necessary to adequately conduct
a study to estimate the population mean to
within 5 points. The range of population
values is 80 and the researcher plans to use a
90% level of confidence. The sample size
should be at least _______.
a) 44
b) 62
c) 216
d) 692
e) 700
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75. A study is going to be conducted in
which a population mean will be estimated
using a 92% confidence interval. The
estimate needs to be within 12 of the actual
population mean. The population variance is
estimated to be around 2500. The necessary
sample size should be at least _______.
a) 15
b) 47
c) 54
d) 638
e) 700
76. In estimating the sample size necessary
to estimate p, if there is no good
approximation for the value of p available,
the value of ____ should be used as an
estimate of p in the formula.
a) 0.10
b) 0.50
c) 0.40
d) 1.96
e) 2.00
77. A researcher wants to estimate the
population proportion with a 95% level of
confidence. He estimates from previous
studies that the population proportion is no
more than .30. The researcher wants the
estimate to have an error of no more than
.03. The necessary sample size is at least
_______.
a) 27
b) 188
c) 211
d) 897
e) 900
78. Catherine Chao, Director of Marketing
Research, is evaluating consumer
acceptance of a new toothpaste package.
She plans to use a 95% confidence interval
estimate of the proportion of households
which prefer the new packages; she will
accept a 0.05 error. Previous studies
indicate that new packaging has an
approximately 70% acceptance rate. The
sample size should be at least _______.
a) 27
b) 59
c) 323
d) 427
e) 500
79. A researcher wants to estimate the
population proportion with a 90% level of
confidence. She estimates from previous
studies that the population proportion is no
more than .30. The researcher wants the
estimate to have an error of no more than
.02. The necessary sample size is at least
_______.
a) 29
b) 47
c) 298
d) 1421
e) 1500
80. A study will be conducted to estimate
the population proportion. A level of
confidence of 99% will be used and an error
of no more than .04 is desired. There is no
knowledge as to what the population
proportion will be. The size of sample
should be at least _______.
a) 1036
b) 160
c) 41
d) 259
e) 289
81. A study is going to be conducted in
which a mean of a lifetime of batteries
produced by a certain method will be
estimated using a 90% confidence interval.
The estimate needs to be within ±2 hours of
MS1023 Business Statistics with Computer Applications Homework #3
Maho Sonmez [email protected] 13
the actual population mean. The population
standard deviation is estimated to be
around 25. The necessary sample size
should be at least _______.
a) 100
b) 21
c) 923
d) 35
e) 423
82. If the population data is normally
distributed and its standard deviation, , is
known, interval estimates for the population
mean must be determined using z-values
regardless of the sample size, n.
a) True
b) False
83. Assumptions underlying the use of t-
statistic in sample-based estimation are that
the population is normally distributed and
population standard deviation is unknown.
a) False
b) True
84. In determining the interval estimates for
a population proportion using the sample
proportion, it is appropriate to use the values
from a t-distribution rather than the z-
distribution.
a) True
b) False
85. A random sample of size 70 is taken
from a population that has a variance of 49.
The sample mean is 90.4. What is the point
estimate of µ?
a) 70
b) 49
c) 90.4
d) 88.76
e) 92.04
86. A random sample of size 70 is taken
from a population that has a variance of 49.
The sample mean is 90.4. A 94% confidence
interval for µ is ___________.
a) 88.76 to 92.04
b) 88.25 to 92.56
c) 79.39 to 101.4
d) 88.83 to 91.97
e) 89.02 to 91.78
87. The average total dollar purchase at a
convenience store is less than that at a
supermarket. Despite smaller-ticket
purchases, convenience stores can still be
profitable because of the size of operation,
volume of business, and the markup. A
researcher is interested in estimating the
average purchase amount for convenience
stores in suburban Long Island. To do so,
she randomly sampled 24 purchases from
several convenience stores in suburban Long
Island and tabulated the amounts to the
nearest dollar (shown below).
$2 $11 $8 $7 $9 $3
$5 $4 $2 $1 $10 $8
$14 $7 $6 $3 $7 $2
$4 $1 $3 $6 $8 $4
Assume that the population standard
deviation is 3.23 and the population is
normally distributed.
Using the above data, a 90% confidence
interval for the population average amount
of purchases is ____________.
a) 4.54 to 6.71
b) 4.495 to 6.76
c) 4.44 to 6.81
d) 4.49 to 6.76
e) 4.26 to 6.99
MS1023 Business Statistics with Computer Applications Homework #3
Maho Sonmez [email protected] 14
88. A meat-processing company in the
Midwest produces and markets a package of
eight small sausage sandwiches. The product
is nationally distributed, and the company is
interested in knowing the average retail
price charged for this item in stores across
the country. The company cannot justify a
national census to generate this information.
Based on the company information system’s
list of all retailers who carry the product, a
researcher for the company contacts 36 of
these retailers and ascertains the selling
prices for the product.
$2.23 $2.11 $2.12 $2.20 $2.17 $2.10
$2.16 $2.31 $1.98 $2.17 $2.14 $1.82
$2.12 $2.07 $2.17 $2.30 $2.29 $2.19
$2.01 $2.24 $2.18 $2.18 $2.32 $2.02
$1.99 $1.87 $2.09 $2.22 $2.15 $2.19
$2.23 $2.10 $2.08 $2.05 $2.16 $2.26
Use the above price data and assume a
population standard deviation of 0.113. A
92% confidence interval to estimate this
price is ___________.
a) 2.11 to 2.18
b) 2.10 to 2.17
c) 2.09 to 2.19
d) 2.11 to 2.17
e) 2.10 to 2.18
89. A random sample of 15 items is taken,
producing a sample mean of 2.364 with a
sample variance of .81.Assume x is
normally distributed and construct a 98%
confidence interval for the population mean.
The 98% confidence interval is _______.
a) 2.320 to 2.408
b) 2.303 to 2.425
c) 1.815 to 2.913
d) 1.790 to 2.937
e) 2.300 to 2.428
90. Some fast-food chains offer a lower-
priced combination meal in an effort to
attract budget-conscious customers. One
chain test-marketed a burger, fries, and a
drink combination for $1.71. The weekly
sales volume for these meals was
impressive. Suppose the chain wants to
estimate the average amount its customers
spent on a meal at their restaurant while this
combination offer was in effect. An analyst
gathers data from 28 randomly selected
customers. The following data represent the
sample meal totals.
$3.21 $5.40 $3.50 $4.39 $5.60 $8.65
$5.02 $4.20 $1.25 $7.64 $3.28 $5.57
$3.26 $3.80 $5.46 $9.87 $4.67 $5.86
$3.73 $4.08 $5.47 $4.49 $5.19 $5.82
$7.62 $4.83 $8.42 $9.10
Assume the amounts spent are normally
distributed. These data were used to
construct a 90% confidence interval to
estimate the population mean value, which
is _______________.
a) 4.69 to 5.98
b) 4.72 to 5.95
c) 4.55 to 6.12
d) 4.57 to 6.10
e) 4.68 to 5.99
91. What proportion of pizza restaurants that
are primarily for walk-in business have a
salad bar? Suppose that, in an effort to
determine this figure, a random sample of
1,250 of these restaurants across the United
States based on the Yellow Pages is called.
If 997 of the restaurants sampled have a
salad bar, what is the 98% confidence
interval for the population proportion?
a) 0.76278 to 0.81642
MS1023 Business Statistics with Computer Applications Homework #3
Maho Sonmez [email protected] 15
b) 0.77368 to 0.82632
c) 0.77891 to 0.81629
d) 0.77533 to 0.81987
e) 0.77116 to 0.82404
92. What proportion of commercial airline
pilots are more than 40 years of age?
Suppose a researcher has access to a list of
all pilots who are members of the
Commercial Airline Pilots Association. If
this list is used as a frame for the study, she
can randomly select a sample of pilots,
contact them, and ascertain their ages. From
89 of these pilots so selected, she learns that
48 are more than 40 years of age. Construct
an 85% confidence interval to estimate the
population proportion of commercial airline
pilots who are more than 40 years of age.
The 85% confidence interval is _______.
a) 0.37353 to 0.52534
b) 0.46327 to 0.61538
c) 0.43577 to 0.64288
d) 0.45242 to 0.62623
e) 0.47161 to 0.60704
93. A bank officer wants to determine the
amount of the average total monthly
deposits per customer at the bank. He
believes an estimate of this average amount
using a confidence interval is sufficient.
How large a sample should he take to be
within $200 of the actual average with 99%
confidence? He assumes the standard
deviation of total monthly deposits for all
customers is about $1,000.
a) 165
b) 166
c) 167
d) 168
e) 169
94. A group of investors wants to develop a
chain of fast-food restaurants. In
determining potential costs for each facility,
they must consider, among other expenses,
the average monthly electric bill. They
decide to sample some fast-food restaurants
currently operating to estimate the monthly
cost of electricity. They want to be 90%
confident of their results and want the error
of the interval estimate to be no more than
$100. They estimate that such bills range
from $600 to $2,500. How large a sample
should they take?
a) 12
b) 13
c) 14
d) 15
e) 16
95. What proportion of secretaries of
Fortune 500 companies has a personal
computer at his or her workstation? You
want to answer this question by conducting
a random survey. How large a sample
should you take if you want to be 95%
confident of the results and you want the
error of the confidence interval to be no
more than .05? Assume no one has any idea
of what the proportion actually is.
a) 384
b) 385
c) 386
d) 387
e) 388
96. Suppose you want to estimate the
proportion of cars that are sport utility
vehicles (SUVs) being driven in Kansas
City, Missouri, at rush hour by standing on
the corner of I-70 and I-470 and counting
SUVs. You believe the figure is no higher
MS1023 Business Statistics with Computer Applications Homework #3
Maho Sonmez [email protected] 16
than .40. If you want the error of the
confidence interval to be no greater than .03,
how many cars should you randomly
sample? Use a 90% level of confidence.
a) 725
b) 724
c) 723
d) 722
e) 721
97. According to a survey by Topaz
Enterprises, a travel auditing company, the
average error by travel agents is $128.
Suppose this figure was obtained from a
random sample of 41 travel agents and the
sample standard deviation is $21. Compute a
98% confidence interval for the national
average error based on these sample results.
Assume the travel agent errors are normally
distributed in the population. How wide is
the interval?
a) 120.46 to 135.54
b) 120.16 to 135.84
c) 120.37 to 135.63
d) 122.48 to 133.52
e) 120.05 to 135.95
According to a survey by Runzheimer
International, the average cost of a fast-food
meal (quarter-pound cheeseburger, large
fries, medium soft drink, excluding taxes) in
Seattle is $4.82. Suppose this figure was
based on a sample of 27 different
establishments and the standard deviation
was $0.37. Assume the costs of a fast-food
meal in Seattle are normally distributed.
Answer questions 98-99 based on the above
information.
98. What is the 95% confidence interval for
the population mean cost for all fast-food
meals in Seattle?
a) 4.08 to 5.56
b) 4.68 to 4.96
c) 4.67 to 4.97
d) 4.70 to 4.94
e) 4.69 to 4.94
99. Using the confidence interval as a guide,
is it likely that the population mean is really
$4.50? Why or why not?
a) Yes, because $4.5 is inside the interval.
b) Yes, because $4.5 is outside the interval.
c) No, because $4.5 is inside the interval.
d) No, because $4.5 is outside the interval.
e) None of the above.
100. A regional survey of 561 companies
asked the vice president of operations how
satisfied he or she was with the software
support received from the computer staff of
the company. Suppose 187 of the 561 vice
presidents said they were satisfied. What is
the 99% confidence interval for the
proportion of the population of vice
presidents who would have said they were
satisfied with the software support if a
census had been taken?
a) 0.2821 to 0.3846
b) 0.2943 to 0.3723
c) 0.3006 to 0.3661
d) 0.2985 to 0.3682
e) 0.2959 to 0.3708
