Basic Statistics for Business and Economics Douglas Lind 9th Edition – Test Bank
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Sample Test
Basic Statistics for Business and Economics, 9e (Lind)
Chapter 3 Describing Data: Numerical Measures
1) A value that “attempts to pinpoint the center of a
distribution of data” is referred to as a measure of location.
Answer: TRUE
Explanation: The purpose of a measure of location is to
pinpoint the center of a distribution of data. An average is a measure of
location that shows the central value of the data. Four measures of location
are discussed in the text: the arithmetic mean, the median, the mode, and the
geometric mean.
Difficulty: 1 Easy
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
2) The arithmetic mean is calculated as the sum of the values,
divided by the total number of values observed.
Answer: TRUE
Explanation: This is the formula for calculating the
arithmetic mean. It can be used to calculate either population means (for
populations) or sample means (for samples).
Difficulty: 1 Easy
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
3) For a set of data arranged or sorted in numerical order, the
value of the observation in the center is called the weighted mean.
Answer: FALSE
Explanation: The median is the midpoint of the values
after they have been ordered from the minimum to the maximum values.
Difficulty: 1 Easy
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
4) A set of ordinal-, interval-, or ratio-level data may have
only one mode.
Answer: FALSE
Explanation: A set of observations may have more than one
mode. For example, the following set of data has two modes, 3 and 7: 1, 2, 3,
3, 3, 4, 4, 5, 7, 7, 7, 10.
Difficulty: 1 Easy
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
5) The mode is the value of the observation that appears most
frequently.
Answer: TRUE
Explanation: This is the definition of the mode.
Difficulty: 1 Easy
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
6) Extremely high or low scores affect the value of the median.
Answer: FALSE
Explanation: A median is the middle observation in a
sorted list of data. High or low values do not have any effect on the median.
Arithmetic means are impacted by high or low values, however.
Difficulty: 2 Medium
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
7) The sum of the deviations of each value (For example: 4, 9,
and 5) from the mean of those values, is zero.
Answer: TRUE
Explanation: This is a basic property of the arithmetic
mean, that the sum of deviations away from the mean is zero. The mean of this
data set is (4 + 9 + 5)/3 = 6. The deviations from this mean are 4 − 6 = −2, 9
− 6 = +3, and 5 − 6 = −1. The sum of the deviations from the mean are −2 + 3 −
1 = 0.
Difficulty: 2 Medium
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
8) Ten people are sampled. Three (3) of them earn $8 an hour,
six (6) of them earn $9 an hour, and one (1) of them earns $12 an hour. The
weighted mean of the hourly wages is $9.
Answer: TRUE
Explanation: The weighted mean,
Difficulty: 2 Medium
Topic: The Weighted Mean
Learning Objective: 03-02 Compute a weighted mean.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
9) For any set of data, there is an equal number of values above
and below the mean.
Answer: FALSE
Explanation: There is an equal number of observations
above and below the median.
Difficulty: 2 Medium
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
10) The variance is the arithmetic mean of the squared
deviations from the median.
Answer: FALSE
Explanation: The variance is the arithmetic mean of the
squared deviations from the mean.
Difficulty: 1 Easy
Topic: Why Study Dispersion?
Learning Objective: 03-03 Compute and interpret the range,
variance, and standard deviation.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
11) The standard deviation is the square root of the variance.
Answer: TRUE
Explanation: The variance must be a positive number as it
is based on the squared deviations from the mean. The standard deviation is the
square root of the variance.
Difficulty: 1 Easy
Topic: Why Study Dispersion?
Learning Objective: 03-03 Compute and interpret the range,
variance, and standard deviation.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
12) For any data set, Chebyshev’s theorem estimates the
proportion of the values that lie within k standard deviations of the mean,
where k is
greater than 1.0.
Answer: TRUE
Explanation: Chebyshev’s theorem says that for any set of
observations in a population or a sample, the proportion of the values that lie
within k standard
deviations of the mean is at least 1 − 1/k2,
where k >
1.
Difficulty: 2 Medium
Topic: Interpretation and Uses of the Standard Deviation
Learning Objective: 03-04 Explain and apply Chebyshevs
theorem and the Empirical Rule.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
13) In a company, the standard deviation of the ages of female
employees is 6 years and the standard deviation of the ages of male employees
is 10 years. These statistics indicate that the dispersion of age is greater
for females than for males.
Answer: FALSE
Explanation: The standard deviation of age for males is
larger, indicating there is more dispersion among the males.
Difficulty: 2 Medium
Topic: Why Study Dispersion?
Learning Objective: 03-03 Compute and interpret the range,
variance, and standard deviation.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
14) According to the Empirical rule, about 95% of the
observations lie within plus and minus two standard deviations of the mean.
Answer: TRUE
Explanation: The Empirical rule states that about 95% of
observations will lie within two standard deviations above and two standard
deviations below the mean.
Difficulty: 2 Medium
Topic: Interpretation and Uses of the Standard Deviation
Learning Objective: 03-04 Explain and apply Chebyshevs
theorem and the Empirical Rule.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
15) The sum of the deviations of each data value from this
measure of location will always be zero.
1. A)
Mode
2. B)
Mean
3. C)
Median
4. D)
Standard deviation
Answer: B
Explanation: The sum of the deviations for values less
than the mean is equal to the sum of the deviations for values greater than the
mean.
Difficulty: 1 Easy
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
16) For any data set, which of the following measures of
location have only one value?
1. A)
Mode and median
2. B)
Mode and mean
3. C)
Mode and standard deviation
4. D)
Mean and median
Answer: D
Explanation: A set of data can have only one value for the
mean and median. A data set can have more than one value for the mode or no
mode at all.
Difficulty: 1 Easy
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
17) Which measures of location are not affected by extremely
small or extremely large values?
1. A)
Mean and median
2. B)
Mean and mode
3. C)
Mode and median
4. D)
Standard deviation and mean
Answer: C
Explanation: The mean is affected by large and small values.
A median is the middle observation in a sorted list of data. The values do not
have any effect on the median. The mode is the value that occurs most
frequently.
Difficulty: 1 Easy
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
18) What is the relationship among the mean, median, and mode in
a symmetric distribution?
1. A)
They are all equal.
2. B)
The mean is always the smallest value.
3. C)
The mean is always the largest value.
4. D)
The mode is the largest value.
Answer: A
Explanation: In a symmetric distribution, the mean,
median, and mode are located at the center and are always equal.
Difficulty: 2 Medium
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
19) For a data set, half of the observations are always greater
than the ________.
1. A)
median
2. B)
mode
3. C)
mean
4. D)
standard deviation
Answer: A
Explanation: Half of the observations will be larger than
the median and half smaller. This is not necessarily true of the mean and mode.
Difficulty: 1 Easy
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
20) What is the lowest level of measurement for which a median
can be determined?
1. A)
Nominal
2. B)
Ordinal
3. C)
Interval
4. D)
Ratio
Answer: B
Explanation: For the median, the data must be at least an
ordinal level of measurement.
Difficulty: 2 Medium
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
21) Which of the following mathematical symbols refers to the
population mean?
1. A) µ
2. B) s
3. C) σ
4. D) χ
Answer: A
Explanation: The Greek letter µ identifies the population
mean. Generally, Greek letters refer to population parameters.
Difficulty: 1 Easy
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
22) On a finance exam, 15 accounting majors had an average grade
of 90. On the same exam, 7 marketing majors averaged 85, and 10 finance majors
averaged 93. What is the weighted mean for all 32 students taking the exam?
89.
A) 89.84
90.
B) 89.33
91.
C) 89.48
92.
D) 10.67
Answer: A
Explanation: Multiply the average grade for each of the
majors by the number of majors, sum the results, and finally divide the total
by 32. [(15 × 90) + (7 × 85) + (10 × 93)]/(15 + 7 + 10) = 89.84.
Difficulty: 2 Medium
Topic: The Weighted Mean
Learning Objective: 03-02 Compute a weighted mean.
Bloom’s: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
23) A survey item asked students to indicate their class rank in
college: freshman, sophomore, junior, or senior. Which measure(s) of location
would be appropriate for the data generated by that questionnaire item?
1. A)
Mean and median
2. B)
Mean and mode
3. C)
Mode and median
4. D)
Mode only
Answer: C
Explanation: Class rank is ordinal scale, so the mode and
median are appropriate.
Difficulty: 2 Medium
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
24) What is the median of 26, 30, 24, 32, 32, 31, 27, and 29?
1. A) 32
2. B) 29
3. C) 30
4. D)
29.5
Answer: D
Explanation: The observations are first ordered from
smallest to largest: 24, 26, 27, 29, 30, 31, 32, 32. Then by convention to
obtain a unique value, we calculate the mean of the two middle observations.
The two middle observations are 29 and 30. The mean of 29 and 30 is 29.5.
Difficulty: 2 Medium
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
25) The net incomes (in $millions) of a sample of steel
fabricators are $86, $67, $86, and $85. What is the mode of the net income?
1. A)
$67
2. B)
$85
3. C)
$85.5
4. D)
$86
Answer: D
Explanation: The mode is the value of the observation that
appears most frequently. The value $86 is the only value that appears more than
once.
Difficulty: 1 Easy
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
26) A stockbroker placed the following order for a customer:
- 50
shares of Kaiser Aluminum at $104 a share
- 100
shares of GTE at $25.25 a share
- 20
shares of Boston Edison at $9.125 a share
What is the weighted arithmetic mean price per share?
25.
A) $25.25
26.
B) $79.75
27.
C) $103.50
28.
D) $46.51
Answer: D
Explanation: Multiply the number of shares by the share
price for each stock and sum the results. Divide this result by 170, the total
number of shares ordered. [(50 × 104) + (100 × 25.25) + (20 × 9.125)]/(50 + 100
+ 20) = 46.51.
Difficulty: 3 Hard
Topic: The Weighted Mean
Learning Objective: 03-02 Compute a weighted mean.
Bloom’s: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
27) During the past six months, a purchasing agent placed the
following three orders for coal:
|
|
|
|
|
|
|
|
|||||||||
|
Tons of Coal |
|
1,200 |
|
|
|
3,000 |
|
|
|
500 |
|
||||
|
Price Per Ton |
$ |
28.50 |
|
|
$ |
87.25 |
|
|
$ |
88.00 |
|
||||
What is the weighted arithmetic mean price per ton?
87.
A) $87.25
88.
B) $72.33
89.
C) $68.47
90.
D) $89.18
Answer: B
Explanation: Multiply the tons of coal purchased by the
price per ton and sum the results. Divide this result by 4,700, the total tons
purchased. [(1,200 × 28.5) + (3,000 × 87.25) + (500 × 88.00)]/(1,200 + 3,000 +
500) = 72.33.
Difficulty: 3 Hard
Topic: The Weighted Mean
Learning Objective: 03-02 Compute a weighted mean.
Bloom’s: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
28) A sample of single persons receiving Social Security
payments revealed these monthly benefits: $826, $699, $1,087, $880, $839, and
$965. How many observations are below the median?
1. A) 1
2. B) 2
3. C) 3
4. D)
3.5
Answer: C
Explanation: Order the six observations from smallest to
largest: 699, 826, 839, 880, 965, 1,087. The median is the mean of the two
middle observations (839 and 880), or 859.5. There are three observations
smaller than this value.
Difficulty: 2 Medium
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
29) Over the last six months, the following numbers of absences
have been reported: 6, 0, 10, 14, 8, and 0. What is the median number of
monthly absences?
1. A) 6
2. B) 7
3. C) 8
4. D) 3
Answer: B
Explanation: Order the six observations from smallest to
largest: 0, 0, 6, 8, 10, 14. The median value is the mean of the two middle
observations (6 and 8). The median is 7.
Difficulty: 2 Medium
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
30) Assume a student received the following grades for the
semester: History, B; Statistics, A; Spanish, C; and English, C. History and
English are 5 credit-hour courses, Statistics a 4 credit-hour course, and
Spanish is a 3 credit-hour course. If 4 grade points are assigned for an A, 3
for a B, and 2 for a C, what is the weighted mean grade for the semester?
4. A)
4.00
5. B)
1.96
6. C)
2.76
7. D)
3.01
Answer: C
Explanation: Multiply the semester hours per class by the
points earned, sum the results, and divide the total by 17, or [(4 × 4) + (5 ×
3) + (8 × 2)]/(4 + 5 + 8) = 2.76.
Difficulty: 3 Hard
Topic: The Weighted Mean
Learning Objective: 03-02 Compute a weighted mean.
Bloom’s: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
31) A sample of the paramedical fees charged by clinics revealed
these amounts: $55, $49, $50, $45, $52, and $55. What is the median charge?
47.
A) $47.50
48.
B) $51.00
49.
C) $52.00
50.
D) $55.00
Answer: B
Explanation: Order these six observations from smallest to
largest: 45, 49, 50, 52, 55, 55. The median value is the mean of the two middle
observations (50 and 52). The median is $51.00.
Difficulty: 3 Hard
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
32) The times (in minutes) that several underwriters took to
review applications for similar insurance coverage are 50, 230, 52, and 57.
What is the median length of time required to review an application?
54.
A) 54.5
55.
B) 141.0
56.
C) 97.25
57.
D) 109.0
Answer: A
Explanation: Order these four observations from smallest
to largest: 50, 52, 57, 230. The median value is the mean of the two middle
observations (52 and 57). The median is 54.5.
Difficulty: 3 Hard
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
33) A bottling company offers three kinds of delivery service:
instant, same day, and within five days. The profit per delivery varies
according to the kind of delivery. The profit for an instant delivery is less
than the other kinds because the driver has to go directly to a grocery store
with a small load and return to the bottling plant. To find out what effect
each type of delivery has on the profit picture, the company summarized the
data in the following table based on deliveries for the previous quarter.
|
Type of Delivery |
Frequency per Quarter |
Profit per Delivery |
||||
|
Instant |
|
100 |
|
$ |
70 |
|
|
Same day |
|
60 |
|
$ |
100 |
|
|
Within five days |
|
40 |
|
$ |
160 |
|
What is the weighted mean profit per delivery?
1. A)
$72
2. B)
$110
3. C)
$142
4. D)
$97
Answer: D
Explanation: Multiply the numbers of deliveries by the
profit per delivery for each type of service and sum the results. Divide this
result (“Total Profits”) by 200, the total number of deliveries. The weighted
mean profit per delivery is [(100 × 70) + (60 × 100) + (40 × 160)]/[(100 + 60 +
40)] = 97 dollars.
Difficulty: 3 Hard
Topic: The Weighted Mean
Learning Objective: 03-02 Compute a weighted mean.
Bloom’s: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
34) For the most recent seven years, the U.S. Department of
Education reported the following number of bachelor’s degrees awarded in
computer science: 4,033; 5,652; 6,407; 7,201; 8,719; 11,154; 15,121. What is
the annual arithmetic mean number of degrees awarded?
1. A)
About 12,240
2. B)
About 8,327
3. C)
About 6,217
4. D)
About 15,962
Answer: B
Explanation: To find the mean, add the degrees earned for
each of the seven years and divide the total by 7.
Difficulty: 2 Medium
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
35) A question in a market survey asks for a respondent’s
favorite car color. Which measure of location should be used to summarize this
question?
1. A)
Mode
2. B)
Median
3. C)
Mean
4. D)
Standard deviation
Answer: A
Explanation: Car color is the nominal scale of
measurement. The mode is especially useful in summarizing nominal-level data.
Difficulty: 2 Medium
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
36) Sometimes, a data set has two different values that occur
with the greatest frequency. In this case, the distribution of the data can
best be described as ________.
1. A)
symmetric
2. B)
bimodal (having two modes)
3. C)
positively skewed
4. D)
negatively skewed
Answer: B
Explanation: The distribution is bimodal.
Difficulty: 2 Medium
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
37) A disadvantage of using an arithmetic mean to summarize a
set of data is that ________.
1. A)
the arithmetic mean sometimes has two values
2. B) it
can be used for interval and ratio data
3. C) it
is always different from the median
4. D) it
can be biased by one or two extremely small or large values
Answer: D
Explanation: The mean uses the value of every item in a
sample, or population, in its computation. If one or two of these values are
either extremely large or extremely small compared to the majority of data, the
mean might not be an appropriate average to represent the data.
Difficulty: 2 Medium
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
38) The mean, as a measure of location, would be inappropriate
for which of the following?
1. A)
Ages of adults at a senior citizen center.
2. B)
Incomes of lawyers.
3. C)
Number of pages in textbooks on statistics.
4. D)
Marital status of college students at a university.
Answer: D
Explanation: Marital status is the nominal scale of
measurement. The mean cannot be calculated for nominal scale data.
Difficulty: 2 Medium
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
39) What is a limitation of the range as a measure of
dispersion?
1. A) It
is based on only two observations.
2. B) It
can be distorted by a large mean.
3. C) It
is not in the same units as the original data.
4. D) It
has no disadvantage.
Answer: A
Explanation: If either the largest or smallest value is an
extreme value, the range is distorted.
Difficulty: 2 Medium
Topic: Why Study Dispersion?
Learning Objective: 03-03 Compute and interpret the range,
variance, and standard deviation.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
40) The sum of the differences between observations and the mean
is equal to ________.
1. A)
zero
2. B)
the mean deviation
3. C)
the range
4. D)
the standard deviation
Answer: A
Explanation: This is one of the properties of the mean.
The sum of the negative differences will “balance” the sum of the positive
differences and will equal zero. It is why the mean can be considered the
balance point of a set of data.
Difficulty: 2 Medium
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
41) If the variance of the “number of daily parking tickets”
issued is 100, the standard deviation is defined as the ________.
1. A)
“number of daily parking tickets”
2. B)
“number of daily parking tickets” squared
3. C)
absolute value of the variance of the “number of daily parking tickets”
4. D)
square root of the variance of the “number of daily parking tickets”
Answer: D
Explanation: The standard deviation is the square root of
the variance. So the standard deviation is 10, found by taking the square root
of the variance, 100.
Difficulty: 2 Medium
Topic: Why Study Dispersion?
Learning Objective: 03-03 Compute and interpret the range,
variance, and standard deviation.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
42) What is the relationship between the variance and the
standard deviation?
1. A)
Variance is the square root of the standard deviation.
2. B)
Variance is the square of the standard deviation.
3. C)
Variance is twice the standard deviation.
4. D)
There is no constant relationship between the variance and the standard
deviation.
Answer: B
Explanation: The square root of the variance is the
standard deviation. Conversely, if you square the standard deviation you will
calculate the variance.
Difficulty: 2 Medium
Topic: Why Study Dispersion?
Learning Objective: 03-03 Compute and interpret the range,
variance, and standard deviation.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
43) According to Chebyshev’s theorem, at least what percent of
the observations lie within plus and minus 1.75 standard deviations of the
mean?
1. A)
56%
2. B)
95%
3. C)
67%
4. D)
100%
Answer: C
Explanation: We use Chebyshev’s theorem, so 1 − [(1/k2)] =
1 − [1/(1.75)2] = 1 − [1/3.0625] = 1 − .3265 = 0.67 (rounded to two
decimal places).
Difficulty: 2 Medium
Topic: Interpretation and Uses of the Standard Deviation
Learning Objective: 03-04 Explain and apply Chebyshevs
theorem and the Empirical Rule.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
44) For a sample of similar-sized all-electric homes, the March
electric bills were (to the nearest dollar): $212, $191, $176, $129, $106, $92,
$108, $109, $103, $121, $175, and $194. What is the range?
1. A)
$100
2. B)
$130
3. C)
$120
4. D)
$112
Answer: C
Explanation: The range is $120, found by the difference
between the largest bill ($212) and the smallest ($92).
Difficulty: 1 Easy
Topic: Why Study Dispersion?
Learning Objective: 03-03 Compute and interpret the range,
variance, and standard deviation.
Bloom’s: Remember
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
45) The following are the weekly amounts of welfare payments
made by the federal government to a sample of six families: $139, $136, $130,
$136, $147, and $136. What is the range?
1. A) $0
2. B)
$14
3. C)
$52
4. D)
$17
Answer: D
Explanation: The range is $17, found by finding the
difference between the largest value ($147) and the smallest ($130).
Difficulty: 1 Easy
Topic: Why Study Dispersion?
Learning Objective: 03-03 Compute and interpret the range,
variance, and standard deviation.
Bloom’s: Remember
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
46) For the past week, a company’s common stock closed with the
following prices: $61.50, $62.00, $61.25, $60.875, and $61.50. What was the
price range?
1. A)
$1.250
2. B)
$1.750
3. C)
$1.125
4. D)
$1.875
Answer: C
Explanation: The range is $1.125, found by finding the
difference between the largest value ($62) and the smallest ($60.875).
Difficulty: 1 Easy
Topic: Why Study Dispersion?
Learning Objective: 03-03 Compute and interpret the range,
variance, and standard deviation.
Bloom’s: Remember
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
47) The monthly amounts spent for food by families of four
receiving food stamps approximates a symmetrical, normal distribution. The
sample mean is $150 and the standard deviation is $20. Using the Empirical
rule, about 95% of the monthly food expenditures are between which of the
following two amounts?
1. A)
$100 and $200
2. B)
$85 and $105
3. C)
$205 and $220
4. D)
$110 and $190
Answer: D
Explanation: The Empirical rule says that 95% of
observations will lie between plus or minus two standard deviations of the
mean, or $150 ± 2($20). The lower value is $110 (= $150 − $40) and the upper
value is $190 (= $150 + $40).
Difficulty: 3 Hard
Topic: Interpretation and Uses of the Standard Deviation
Learning Objective: 03-04 Explain and apply Chebyshevs
theorem and the Empirical Rule.
Bloom’s: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
48) The ages of all the patients in the isolation ward of the hospital
are 38, 26, 13, 41, and 22. What is the population variance?
106.
A) 106.8
107.
B) 91.4
108.
C) 240.3
109.
D) 42.4
Answer: A
Explanation: The mean is (38 + 26 + 13 + 41 + 22)/5 = 28.
Using formula ,
Difficulty: 3 Hard
Topic: Why Study Dispersion?
Learning Objective: 03-03 Compute and interpret the range,
variance, and standard deviation.
Bloom’s: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
49) A sample of assistant professors on the business faculty at
state-supported institutions in Ohio revealed the mean income to be $72,000 for
nine months, with a standard deviation of $3,000. Using Chebyshev’s theorem,
what proportion of the faculty earns more than $66,000, but less than $78,000?
1. A) At
least 50%
2. B) At
least 25%
3. C) At
least 75%
4. D) At
least 100%
Answer: C
Explanation: The end values of $66,000 and $78,000 each
differ from the mean by $6,000. The value $6,000 is two standard deviations
above and below the mean, found by $6,000/$3,000. Using Chebyshev’s theorem: 1
− 1/(2)2 = 0.75.
Difficulty: 3 Hard
Topic: Interpretation and Uses of the Standard Deviation
Learning Objective: 03-04 Explain and apply Chebyshevs
theorem and the Empirical Rule.
Bloom’s: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
50) A population consists of all the weights of all defensive
backs on a university’s football team. They are Johnson, 204 pounds; Patrick,
215 pounds; Junior, 207 pounds; Kendron, 212 pounds; Nicko, 214 pounds; and
Cochran, 208 pounds. What is the population standard deviation (in pounds)?
1. A)
About 4
2. B)
About 16
3. C)
About 100
4. D)
About 40
Answer: A
Explanation: The mean is (204 + 215 + 207 + 212 + 214 +
208) / 6 = 210. Using formula ,
Difficulty: 3 Hard
Topic: Why Study Dispersion?
Learning Objective: 03-03 Compute and interpret the range,
variance, and standard deviation.
Bloom’s: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
51) A sample of small bottles and their contents has the
following weights (in grams): 4, 2, 5, 4, 5, 2, and 6. What is the sample
variance of bottle contents weight?
6. A)
6.92
7. B)
4.80
8. C)
1.96
9. D)
2.33
Answer: D
Explanation: The sample mean is (4 + 2 + 5 + 4 + 5 + 2 +
6) / (7 − 1) = 4. Using formula ,
Difficulty: 3 Hard
Topic: Why Study Dispersion?
Learning Objective: 03-03 Compute and interpret the range,
variance, and standard deviation.
Bloom’s: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
52) The distribution of a sample of the outside diameters of PVC
pipes approximates a symmetrical, bell-shaped distribution. The arithmetic mean
is 14.0 inches, and the standard deviation is 0.1 inches. About 68% of the
outside diameters lie between what two amounts?
13.
A) 13.5 and 14.5 inches
14.
B) 13.0 and 15.0 inches
15.
C) 13.9 and 14.1 inches
16.
D) 13.8 and 14.2 inches
Answer: C
Explanation: Based on the Empirical rule, 68% of
observations are within ±1 standard deviation of the mean. The mean is 14.0 and
the standard deviation is 0.1, so the limits are 14.0 ± 0.1. The lower limit is
13.9 inches, and the upper limit is 14.1 inches.
Difficulty: 2 Medium
Topic: Interpretation and Uses of the Standard Deviation
Learning Objective: 03-04 Explain and apply Chebyshevs
theorem and the Empirical Rule.
Bloom’s: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
53) The sample variance of hourly wages was 10. What is the
sample standard deviation?
1. A)
$1.96
2. B)
$4.67
3. C)
$3.16
4. D)
$10.00
Answer: C
Explanation: The standard deviation is the square root of
the variance; the square root of $10 is $3.16.
Difficulty: 2 Medium
Topic: Why Study Dispersion?
Learning Objective: 03-03 Compute and interpret the range,
variance, and standard deviation.
Bloom’s: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
54) Based on the Empirical rule, what percent of the
observations will lie within plus or minus two standard deviations from the
mean?
1. A)
95%
2. B) 5%
3. C)
68%
4. D)
2.5%
Answer: A
Explanation: Based on the Empirical rule, 95% of the
observations are within two standard deviations of the mean.
Difficulty: 2 Medium
Topic: Interpretation and Uses of the Standard Deviation
Learning Objective: 03-04 Explain and apply Chebyshevs
theorem and the Empirical Rule.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
55) A sample of wires coming off the production line was tested
for tensile strength. The statistical results (in PSI) were the following:
|
Arithmetic mean |
500 |
Median |
500 |
|
Mode |
500 |
Standard deviation |
40 |
|
Quartile deviation |
25 |
Mean deviation |
32 |
|
Range |
240 |
Sample size |
100 |
According to the Empirical rule, 95% of the wires tested had a
tensile strength between approximately which of the following two values?
1. A)
450 and 550
2. B)
460 and 540
3. C)
420 and 580
4. D)
380 and 620
Answer: C
Explanation: Based on the Empirical rule, 95% of
observations are within ±2 standard deviation of the mean. The mean is 500 and
the standard deviation is 40, so the limits are 500 ± 80. The lower limit is
420 inches, and the upper limit is 580 inches.
Difficulty: 2 Medium
Topic: Interpretation and Uses of the Standard Deviation
Learning Objective: 03-04 Explain and apply Chebyshevs
theorem and the Empirical Rule.
Bloom’s: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
56) Consider two populations with the same mean. Since they have
the same mean, then ________.
1. A)
their standard deviations must also be the same
2. B)
their medians must also be the same
3. C)
their modes must also be the same
4. D)
None of these is correct.
Answer: D
Explanation: The mean, median, and mode will only be the
same if both populations are perfectly symmetric. Here, we do not know whether
the populations are symmetric, only that they have the same mean. Consider two
nonsymmetrical populations A and B. Suppose Population A has the following
values: 1, 2, 2, 4, 11. The mean of this population is 4, the median is 2, and
the mode is 2. Suppose Population B has the following values: 1, 1, 5, 6, 7.
The mean of this population is also 4, but the median is 5 and the mode is 1.
Difficulty: 2 Medium
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
57) The sample mean ________.
1. A) is
always equal to the population mean.
2. B) is
always smaller than the population mean.
3. C) is
found by adding the data values and dividing them by (n − 1).
4. D) is
found by adding all data values and dividing them by n.
Answer: D
Explanation: The sample mean is found by adding up all
data values in the sample and dividing by n, the number in the sample.
Sample Mean .
Population means are found by adding up all data values in the population
and dividing by N,
the number in the population.
Population Mean .
Difficulty: 2 Medium
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
58) The variance of a sample of 121 observations equals 441. The
standard deviation of the sample equals ________.
1. A) 11
2. B) 21
3. C)
1.91
4. D)
231
Answer: B
Explanation: The standard deviation is the square root of
the variance of 441, which is 21.
Difficulty: 1 Easy
Topic: Why Study Dispersion?
Learning Objective: 03-03 Compute and interpret the range,
variance, and standard deviation.
Bloom’s: Remember
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
59) When computing the arithmetic mean, the smallest value in
the data set ________.
1. A)
can never be negative
2. B)
can never be zero
3. C)
can never be less than the mean
4. D)
can be any value
Answer: D
Explanation: When computing an arithmetic mean, we sum all
of the values (in the population or sample) and divide by the number of values.
The values can be negative or positive numbers. The smallest value can be any
value, but it will be less than the mean unless all the values in the data set
are the same.
Difficulty: 1 Easy
Topic: Measures of Location
Learning Objective: 03-01 Compute and interpret the mean,
the median, and the mode.
Bloom’s: Remember
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
Basic Statistics for Business and Economics, 9e (Lind)
Chapter 5 A Survey of Probability Concepts
1) The probability of rolling a 3 or 2 on a single die is an
example of conditional probability.
Answer: FALSE
Explanation: This is an example of classical probability.
Classical probability is based on the assumption that the outcomes of an
experiment (e.g. rolling a die) are equally likely. Conditional probability is
the probability of a particular event occurring, given that another event has
occurred (covered under LO5-4).
Difficulty: 2 Medium
Topic: Rules of Multiplication to Calculate Probability
Learning Objective: 05-02 Assign probabilities using a
classical, empirical, or subjective approach.; 05-04 Calculate probabilities
using the rules of multiplication.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
2) The probability of rolling a 3 or 2 on a single roll of a die
is an example of mutually exclusive events.
Answer: TRUE
Explanation: This is mutually exclusive as you cannot roll
both 2 and 3 at the same time. Only one of these events can happen on a single
roll of a die.
Difficulty: 2 Medium
Topic: Approaches to Assigning Probabilities
Learning Objective: 05-02 Assign probabilities using a
classical, empirical, or subjective approach.
Bloom’s: Understand
AACSB: Communication
Accessibility: Keyboard Navigation
3) An individual can assign a subjective probability to an event
based on whatever information is available.
Answer: TRUE
Explanation: When an individual evaluates the available
opinions and information and then estimates or assigns the probability. This
probability is called subjective probability.
Difficulty: 1 Easy
Topic: Approaches to Assigning Probabilities
Learning Objective: 05-02 Assign probabilities using a
classical, empirical, or subjective approach.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
4) To apply the special rule of addition, the events must be mutually
exclusive.
Answer: TRUE
Explanation: The special rule of addition requires that
events be mutually exclusive. As illustrated using a Venn diagram, this occurs
when there is no intersection or overlap of events. Since the events cannot
occur concurrently, the joint probability is zero.
Difficulty: 1 Easy
Topic: Rules of Addition for Computing Probabilities
Learning Objective: 05-03 Calculate probabilities using
the rules of addition.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
5) A joint probability measures the likelihood that two or more
events will happen concurrently.
Answer: TRUE
Explanation: A joint probability measures the chance that
two or more events can happen at the same time. If the events are mutually
exclusive, the joint probability is zero.
Difficulty: 1 Easy
Topic: Rules of Addition for Computing Probabilities
Learning Objective: 05-03 Calculate probabilities using
the rules of addition.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
6) The joint probability of two independent events, A and B, is
computed as P(A and B) = P(A) × P(B).
Answer: TRUE
Explanation: For two independent events (A and B), the
probability that A and B will both occur is found by multiplying the two
probabilities. This is the special rule of multiplication.
Difficulty: 1 Easy
Topic: Rules of Multiplication to Calculate Probability
Learning Objective: 05-04 Calculate probabilities using
the rules of multiplication.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
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