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商务统计学笔试复习题

一、The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a videocassette recorder made by the company over the past 12 months are satisfied with their products.

1., the population of interest is

a)all the customers who have bought a videocassette recorder made by the

company over the past 12 months.

b)all the customers who have bought a videocassette recorder made by the

company and brought it in for repair over the past 12 months.

c)all the customers who have used a videocassette recorder over the past 12

months.

d)all the customers who have ever bought a videocassette recorder made by the

company.

ANSWER:

a

2., which of the following will be a good frame for drawing a sample?

a)Telephone directory.

b)Voting registry.

c)The list of customers who returned the registration card.

d) A list of potential customers purchased from a database marketing company.

ANSWER:

c

3.the possible responses to the question "How many videocassette recorders made by

other manufacturers have you used?" are values from a

a)discrete random variable.

b)continuous random variable.

c)categorical random variable.

d)parameter.

ANSWER:

a

4.the possible responses to the question "Are you happy, indifferent, or unhappy with

the performance per dollar spent on the videocassette recorder?" are values from a

a)discrete numerical random variable.

b)continuous numerical random variable.

c)categorical random variable.

d)parameter.

ANSWER:

c

TYPE: MC DIFFICULTY: Easy

KEYWORDS: categorical random variable, types of data

5.the possible responses to the question "What is your annual income rounded to the

nearest thousands?" are values from a

a)discrete numerical random variable.

b)continuous numerical random variable.

c)categorical random variable.

d)parameter.

ANSWER:

a

6.the possible responses to the question "How much time do you use the videocassette

recorder every week on the average?" are values from a

a)discrete numerical random variable.

b)continuous numerical random variable.

c)categorical random variable.

d)parameter.

ANSWER:b

7.the possible responses to the question "How many people are there in your

household?" are values from a

a)discrete numerical random variable.

b)continuous numerical random variable.

c)categorical random variable.

d)parameter.

ANSWER:a

8.the possible responses to the question "How would you rate the quality of your

purchase experience with 1 = excellent, 2 = good, 3 = decent, 4 = poor, 5 = terrible?"

are values from a

a)discrete numerical random variable.

b)continuous numerical random variable.

c)categorical random variable.

d)parameter.

ANSWER: c

9.the possible responses to the question "What brand of videocassette recorder did you

purchase?" are values from a

a)discrete numerical random variable.

b)continuous numerical random variable.

c)categorical random variable.

d)parameter.

ANSWER:c

10.the possible responses to the question "Out of a 100 point score with 100 being the

highest and 0 being the lowest, what is your satisfaction level on the videocassette

recorder that you purchased?" are values from a

a)discrete numerical random variable.

b)continuous numerical random variable.

c)categorical random variable.

d)parameter.

ANSWER:a

11.the possible responses to the question "In which year were you born?" are values

from a

a)discrete numerical random variable.

b)continuous numerical random variable.

c)categorical random variable.

d)parameter.

ANSWER:a

二、The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the proportion of students at her university who visited campus bars on the weekend before the final exam week. Her assistant took a random sample of 250 students. The total number of students in the sample who visited campus bars on the weekend before the final exam week is an example of

e) a categorical random variable.

f) a discrete random variable.

g) a continuous random variable.

h) a parameter.

ANSWER:

b

三、T he chancellor of a major university was concerned about alcohol abuse on her campus

and wanted to find out the proportion of students at her university who visited campus bars on the weekend before the final exam week. Her assistant took a random sample of 250 students and computed the portion of students in the sample who visited campus bars on the weekend before the final exam. The portion of all students at her university who visited campus bars on the weekend before the final exam week is an example of

i) a categorical random variable.

j) a discrete random variable.

k) a continuous random variable.

l) a parameter.

ANSWER:

d

四、T he chancellor of a major university was concerned about alcohol abuse on her campus

and wanted to find out the proportion of students at her university who visited campus bars on the weekend before the final exam week. Her assistant took a random sample of 250 students. The portion of students in the sample who visited campus bars on the weekend before the final exam week is an example of __________.

m) a categorical random variable.

n) a discrete random variable.

o) a parameter.

p) a statistic

ANSWER:

d

五、The ordered array below resulted from taking a sample of 25 batches of 500 computer chips and determining how many in each batch were defective.

Defects

1 2 4 4 5 5 6 7 9 9 12 12 15

17 20 21 23 23 25 26 27 27 28 29 29

1.Referring to Table 2-11, if a frequency distribution for the defects data is constructed,

using "0 but less than 5" as the first class, the frequency of the “20 but less than 25”

class would be ________.

ANSWER:

4

2.Referring to Table 2-11, if a frequency distribution for the defects data is constructed,

using "0 but less than 5" as the first class, the relative frequency of the “15 but less

than 20” class would be ________.

ANSWER:

0.08 or 8% or 2/25

3.Referring to Table 2-11, construct a frequency distribution for the defects data, using

"0 but less than 5" as the first class.

ANSWER:

Defects Frequency

0 but less than 5 4

5 but less than 10 6

10 but less than 15 2

15 but less than 20 2

20 but less than 25 4

25 but less than 30 7

4.Referring to Table 2-11, construct a relative frequency or percentage distribution for

the defects data, using "0 but less than 5" as the first class.

ANSWER:

Defects Percentage

0 but less than 5 16

5 but less than 10 24

10 but less than 15 8

15 but less than 20 8

20 but less than 25 16

25 but less than 30 28

5.Referring to Table 2-11, construct a cumulative percentage distribution for the defects

data if the corresponding frequency distribution uses "0 but less than 5" as the first class.

ANSWER:

Defects C umPct

0 0

5 16

10 40

15 48

20 56

25 72

30 100

6.Referring to Table 2-11, construct a histogram for the defects data, using "0 but less

than 5" as the first class.

ANSWER:

商务统计学笔试复习题

7. Referring to Table 2-11, construct a cumulative percentage polygon for the defects

data if the corresponding frequency distribution uses "0 but less than 5" as the first class.

ANSWER:

Cumulative Percentage Polygon

商务统计学笔试复习题

0%

10%20%30%40%50%60%70%80%90%100%0

5

10

15

20

25

30

Number of Defects

六、Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid and have no private health insurance. The ages of 25 uninsured senior citizens were as follows:

60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92

1. Referring to Table 3-1, calculate the arithmetic mean age of the uninsured senior

citizens to the nearest hundredth of a year.

ANSWER: 74.04 years

2. Referring to Table 3-1, identify the median age of the uninsured senior citizens.

ANSWER: 73 years

3. Referring to Table 3-1, identify the first quartile of the ages of the uninsured senior

citizens.

ANSWER: 65.5 years

4.Referring to Table 3-1, identify the third quartile of the ages of the uninsured senior

citizens.

ANSWER:

81.5 years

5.Referring to Table 3-1, identify the interquartile range of the ages of the uninsured

senior citizens.

ANSWER:

16 years

6.Referring to Table 3-1, identify which of the following is the correct statement.

a)One fourth of the senior citizens sampled are below 65.5 years of age.

b)The middle 50% of the senior citizens sampled are between 65.5 and 73.0

years of age.

c)The average age of senior citizens sampled is 73.5 years of age.

d)All of the above are correct.

ANSWER:

a

7.Referring to Table 3-1, identify which of the following is the correct statement.

a)One fourth of the senior citizens sampled are below 64 years of age.

b)The middle 50% of the senior citizens sampled are between 65.5 and 73.0

years of age.

c)25% of the senior citizens sampled are older than 81.5 years of age.

d)All of the above are correct.

ANSWER:

c

8.Referring to Table 3-1, what type of shape does the distribution of the sample appear

to have?

ANSWER:

Slightly positive or right-skewed.

9.Referring to Table 3-1, calculate the variance of the ages of the uninsured senior

citizens correct to the nearest hundredth of a year squared.

ANSWER:

94.96 years2

10.Referring to Table 3-1, calculate the standard deviation of the ages of the uninsured

senior citizens correct to the nearest hundredth of a year.

ANSWER:

9.74 years

11.Referring to Table 3-1, calculate the coefficient of variation of the ages of the

uninsured senior citizens.

ANSWER:

13.16%

七、The stem-and-leaf display below represents the number of cargo manifests approved by customs inspectors of the Port of New York in a sample of 35 days.

STEM LEAVES

1H 67889

2L 0011122223333444

2H 5566678899

3L 1122

Note (1): 1H means the “high teens” 15, 16, 17, 18, or 19; 2L means the “low

twenties” 20, 21, 22, 23, or 24; 2H means the “high twenties” 25, 26, 27, 28, or 29, etc.

Note (2): For this sample, the sum of the observations is 838, the sum of the squares of the observations is 20,684, and the sum of the squared differences between each

observation and the mean is 619.89.

1.Referring to Table 3-4, the arithmetic mean of the customs data is ________.

ANSWER:

23.9

2.Referring to Table 3-4, the median of the customs data is ________.

ANSWER:

23

3.Referring to Table 3-4, the first quartile of the customs data is ________.

ANSWER:

21

4.Referring to Table 3-4, the third quartile of the customs data is ________.

ANSWER:

27

5.Referring to Table 3-4, the range of the customs data is ________.

ANSWER:

16

6.Referring to Table 3-4, the interquartile range of the customs data is ________.

ANSWER:

6

7.Referring to Table 3-4, the variance of the customs data is ________.

ANSWER:

18.2

8.Referring to Table 3-4, the standard deviation of the customs data is ________.

ANSWER:

4.3

9.Referring to Table 3-4, the coefficient of variation of the customs data is ________

percent.

ANSWER:

17.8% or 18%

10.Referring to Table 3-4, the five-number summary for the data in the customs sample

consists of ________, ________, ________, ________, ________.

ANSWER:

16, 21, 23, 27, 32

11.Referring to Table 3-4, construct a boxplot of this sample.

Box-and-whisker Plot

商务统计学笔试复习题

101520253035

ANSWER:

八、Times spent studying by students in the week before final exams follow a normal

distribution with standard deviation 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students.

1.what is the probability that the sample mean exceeds the population mean by more

than 2 hours?

ANSWER:

0.3085

2.what is the probability that the sample mean is more than 3 hours below the

population mean?

ANSWER:

0.2266

3.what is the probability that the sample mean differs from the population mean by less

than 2 hours?

ANSWER:

0.3829 using Excel or 0.3830 using Table E.2

4.what is the probability that the sample mean differs from the population mean by

more than 3 hours?

ANSWER:

0.4533 using Excel or 0.4532 using Table E.2

九、A quality control engineer is interested in the mean length of sheet insulation being cut

automatically by machine. The desired length of the insulation is 12 feet. It is known that the standard deviation in the cutting length is 0.15 feet. A sample of 70 cut sheets yields a mean length of 12.14 feet. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine.

1.Referring to Table 8-3, the critical value to use in obtaining the confidence interval is

________.

ANSWER:

2.58

2.Referring to Table 8-3, the confidence interval goes from ________ to ________.

ANSWER:

12.09 to 12.19

3.True or False: Referring to Table 8-3, the confidence interval indicates that the

machine is not working properly.

ANSWER:

True

4.True or False: Referring to Table 8-3, the confidence interval is valid only if the

lengths cut are normally distributed.

ANSWER:

False

EXPLANATION: With a sample size of 70, this confidence interval will still be valid if the lengths cut are not normally distributed due to the central limit theorem.

KEYWORDS: confidence interval, mean, standardized normal distribution, central limit theorem

5.Referring to Table 8-3, suppose the engineer had decided to estimate the mean length

to within 0.03 with 99% confidence. Then the sample size would be ________.

ANSWER:

165.8724 rounds up to 166

十、A manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the average owed is $83.40 with a sample standard deviation of $23.65. If you were to conduct a test to determine whether the auditor should conclude that there is evidence that the average balance is different from $75, which test would you use?

a)Z-test of a population mean

b)Z-test of a population proportion

c)t-test of population mean

d)t-test of a population proportion

ANSWER:

c

十一、A manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the average owed is $83.40 with a sample

standard deviation of $23.65. If you wanted to test whether the average balance is different from $75 and decided to reject the null hypothesis, what conclusion could you draw?

e)There is not evidence that the average balance is $75.

f)There is not evidence that the average balance is not $75.

g)There is evidence that the average balance is $75.

h)There is evidence that the average balance is not $75.

ANSWER:

d

十二、The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the inflatable air bags. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30, which test would you use?

i)Z-test of a population mean

j)Z-test of a population proportion

k)t-test of population mean

l)t-test of a population proportion

ANSWER:

b

十三、A student claims that he can correctly identify whether a person is a business major or an agriculture major by the way the person dresses. Suppose in actuality that if someone is a business major, he can correctly identify that person as a business major 87% of the time. When a person is an agriculture major, the student will incorrectly identify that person as a business major 16% of the time. Presented with one person and asked to identify the major of this person (who is either a business or agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the person is a business major and the alternative that the person is an agriculture major.

2.Referring to Table 9-2, what would be a Type I error?

a)Saying that the person is a business major when in fact the person is a

business major.

b)Saying that the person is a business major when in fact the person is an

agriculture major.

c)Saying that the person is an agriculture major when in fact the person is a

business major.

d)Saying that the person is an agriculture major when in fact the person is an

agriculture major.

ANSWER:

c

3.Referring to Table 9-2, what would be a Type II error?

a)Saying that the person is a business major when in fact the person is a

business major.

b)Saying that the person is a business major when in fact the person is an

agriculture major.

c)Saying that the person is an agriculture major when in fact the person is a

business major.

d)Saying that the person is an agriculture major when in fact the person is an

agriculture major.

ANSWER:

b

4.Referring to Table 9-2, what is the “actual level of significance” of the test?

a)0.13

b)0.16

c)0.84

d)0.87

ANSWER:

a

5.Referring to Table 9-2, what is the “actual confidence coefficient”?

a)0.13

b)0.16

c)0.84

d)0.87

ANSWER:

d

6.Referring to Table 9-2, what is the value of α?

a)0.13

b)0.16

c)0.84

d)0.87

ANSWER:

a

7.Referring to Table 9-2, what is the value of β?

a)0.13

b)0.16

c)0.84

d)0.87

ANSWER:

b

十四、Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.

American Japanese

Sample Size 211 100

Mean SSATL Score 65.75 79.83

Population Std. Dev. 11.07 6.41

1.Referring to Table 10-1, judging from the way the data were collected, which test

would likely be most appropriate to employ?

a)Paired t test

b)Pooled-variance t test for the difference between two means

c)Independent samples Z test for the difference between two means

d)Related samples Z test for the mean difference

ANSWER:

c

2.Referring to Table 10-1, give the null and alternative hypotheses to determine if the

average SSATL score of Japanese managers differs from the average SSATL score of American managers.

a)H

0: μ

A

–μ

J

≥0 versus H

1

: μ

A

–μ

J

<0

b)H

0:μ

A

–μ

J

≤0 versus H

1

: μ

A

–μ

J

>0

c)H

0: μ

A

–μ

J

=0 versus H

1

A

–μ

J

≠0

d)H0:X A–X J=0 versus H1:X A–X J≠0

ANSWER:

c

3.Referring to Table 10-1, assuming the independent samples procedure was used,

calculate the value of the test statistic.

a)Z=65.75–79.83 9.82

211

+

9.82

100

b) Z =

65.75–79.83

11.07211+6.41

100

c) Z =

65.75–79.839.822

211+9.82

2

100

d) Z =

65.75–79.8311.072

211+6.41

2

100

ANSWER:

d

4. Referring to Table 10-1, suppose that the test statistic is Z = 2.4

5. Find the p -value if

we assume that the alternative hypothesis was a two-tailed test (0– :1≠J A H μμ).

a) 0.0071 b) 0.0142 c) 0.4929 d)

0.9858

ANSWER: b

十五、An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps as few passengers, on the average, as possible during a month. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the experiment.) The number of passengers bumped each week is obtained, which gives rise to the following Excel output:

ANOVA

Source of Variation SS df MS

F P-value F crit Between Groups 212.4 3 8.304985

0.001474

3.238867

Within Groups 136.4

8.525

Total

348.8

1. Referring to Table 10-15, the within groups degrees of freedom is

e) 3 f) 4 g) 16

h)19

ANSWER:

c

2.Referring to Table 10-15, the total degrees of freedom is

i) 3

j) 4

k)16

l)19

ANSWER:

d

3.Referring to Table 10-15, the among-group (between-group) mean squares is

m)8.525

n)70.8

o)212.4

p)637.2

ANSWER:

b

4.Referring to Table 10-15, at a significance level of 1%,

q)there is insufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are not all the same.

r)there is insufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are all the same.

s)there is sufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are not all the same.

t)there is sufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are all the same.

ANSWER:

c

十六、A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San

Diego County. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status

(Hispanic or non-Hispanic) and (2) seat belt usage (worn or not worn) during the accident.

The number of children in each category is given in the table below.

商务统计学笔试复习题

1.Referring to Table 11-1, the calculated test statistic is

a)-0.9991

b)-0.1368

c)48.1849

d)72.8063

ANSWER:

c

2.Referring to Table 11-1, at 5% level of significance, the critical value of the test

statistic is

a) 3.8415

b) 5.9914

c)9.4877

d)13.2767

ANSWER:

a

3.Referring to Table 11-1, at 5% level of significance, there is sufficient evidence to

conclude that

a)use of seat belts in motor vehicles is related to ethnic status in San Diego

County.

b)use of seat belts in motor vehicles depends on ethnic status in San Diego

County.

c)use of seat belts in motor vehicles is associated with ethnic status in San

Diego County.

d)All of the above.

ANSWER:

d

十七、A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank’s charges (Y) -- measured in dollars per month -- for services rendered to local companies. One independent variable used to predict service charge to a compa ny is the company’s sales revenue (X) -- measured in millions of dollars. Data for 21 companies who use the bank’s services were used to fit the model:

E(Y)=β

0+β

1

X

The results of the simple linear regression are provided below.

2,70020, 65, two-tailed value 0.034 (for testing )YX Y X S p β1

=-+==

1. Referring to Table 12-1, interpret the estimate of β0, the Y -intercept of the line.

a) All companies will be charged at least $2,700 by the bank.

b) There is no practical interpretation since a sales revenue of $0 is a

nonsensical value.

c) About 95% of the observed service charges fall within $2,700 of the least

squares line.

d) For every $1 million increase in sales revenue, we expect a service charge to

decrease $2,700.

ANSWER: b

2. Referring to Table 12-1, interpret the estimate of σ, the standard deviation of the

random error term (standard error of the estimate) in the model.

a) About 95% of the observed service charges fall within $65 of the least

squares line.

b) About 95% of the observed service charges equal their corresponding

predicted values.

c) About 95% of the observed service charges fall within $130 of the least

squares line.

d) For every $1 million increase in sales revenue, we expect a service charge to

increase $65.

ANSWER: c

3. Referring to Table 12-1, interpret the p -value for testing whether β1 exceeds 0.

a) There is sufficient evidence (at the α = 0.05) to conclude that sales revenue

(X ) is a useful linear predictor of service charge (Y ).

b) There is insufficient evidence (at the α = 0.10) to conclude that sales

revenue (X ) is a useful linear predictor of service charge (Y ). c) Sales revenue (X ) is a poor predictor of service charge (Y ).

d) For every $1 million increase in sales revenue, we expect a service charge to

increase $0.034.

ANSWER: a

4. Referring to Table 12-1, a 95% confidence interval for β1 is (15, 30). Interpret the

interval.

a)We are 95% confident that the mean service charge will fall between $15 and

$30 per month.

b)We are 95% confident that the sales revenue (X) will increase between $15

and $30 million for every $1 increase in service charge (Y).

c)We are 95% confident that average service charge (Y) will increase between

$15 and $30 for every $1 million increase in sales revenue (X).

d)At the = 0.05 level, there is no evidence of a linear relationship between

service charge (Y) and sales revenue (X).

ANSWER:

c