MODERN MATHEMATICAL STATISTICS WITH APPLICATIONS 3RD
EDITION – EXAM QUESTIONS AND CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALE | 2027 Q&A | INSTANT DOWNLOAD PDF
1. A population consists of all measurements of interest in a statistical investigation. Which
quantity describes a numerical characteristic of that population?
A. Sample statistic
B. Sampling error
C. Population parameter
D. Observed frequency
Rationale: A population parameter is a numerical characteristic of an entire population, such as
a population mean or variance. A statistic is computed from a sample.
2. A researcher selects 80 students from a university of 8,000 students and records their
daily study hours. The 80 selected students constitute the:
A. Sample
B. Population
C. Parameter
D. Sampling distribution
Rationale: The sample is the subset of individuals actually observed. The population is the full
group of 8,000 students.
3. A variable records the number of defective items found in a shipment. This variable is
best classified as:
A. Continuous quantitative
B. Discrete quantitative
C. Categorical ordinal
D. Continuous qualitative
Rationale: The number of defects is a count and can take only nonnegative integer values,
making it a discrete quantitative variable.
, 4. Which graphical display is particularly appropriate for showing the distribution of a
quantitative variable using intervals of numerical values?
A. Pie chart
B. Bar chart
C. Scatterplot
D. Histogram
Rationale: A histogram groups quantitative observations into intervals and displays their
frequencies or relative frequencies.
5. A sample contains the values 4, 7, 8, 10, and 16. What is the sample mean?
A. 8
B. 8.5
C. 9
D. 10
Rationale: The sample mean is (4 + 7 + 8 + 10 + 16)/5 = 45/5 = 9.
6. Which measure of center is generally least affected by an extremely large or small
observation?
A. Mean
B. Median
C. Range
D. Variance
Rationale: The median depends on the ordered position of observations and is therefore resistant
to extreme values. The mean can be substantially influenced by outliers.
7. For a data set with 12 observations, the sample variance is calculated using which
denominator?
A. 12
B. 11
, C. 13
D. 11 after subtracting the sample mean from each observation
Rationale: The sample variance uses n − 1 degrees of freedom. For n = 12, the denominator is
11.
8. If every observation in a data set is increased by 5, what happens to the sample
variance?
A. It increases by 5.
B. It increases by 25.
C. It remains unchanged.
D. It becomes five times larger.
Rationale: Adding a constant shifts every observation equally but does not change the distances
among observations. Therefore, variance is unchanged.
9. If every observation in a data set is multiplied by 3, the variance is multiplied by:
A. 3
B. 9
C. 6
D. 1/3
Rationale: Variance scales by the square of the multiplication factor. Thus, multiplying
observations by 3 multiplies variance by 3² = 9.
10. A distribution has a long tail extending toward larger values. Which description best
characterizes its shape?
A. Symmetric
B. Left-skewed
C. Uniform
D. Right-skewed
EDITION – EXAM QUESTIONS AND CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALE | 2027 Q&A | INSTANT DOWNLOAD PDF
1. A population consists of all measurements of interest in a statistical investigation. Which
quantity describes a numerical characteristic of that population?
A. Sample statistic
B. Sampling error
C. Population parameter
D. Observed frequency
Rationale: A population parameter is a numerical characteristic of an entire population, such as
a population mean or variance. A statistic is computed from a sample.
2. A researcher selects 80 students from a university of 8,000 students and records their
daily study hours. The 80 selected students constitute the:
A. Sample
B. Population
C. Parameter
D. Sampling distribution
Rationale: The sample is the subset of individuals actually observed. The population is the full
group of 8,000 students.
3. A variable records the number of defective items found in a shipment. This variable is
best classified as:
A. Continuous quantitative
B. Discrete quantitative
C. Categorical ordinal
D. Continuous qualitative
Rationale: The number of defects is a count and can take only nonnegative integer values,
making it a discrete quantitative variable.
, 4. Which graphical display is particularly appropriate for showing the distribution of a
quantitative variable using intervals of numerical values?
A. Pie chart
B. Bar chart
C. Scatterplot
D. Histogram
Rationale: A histogram groups quantitative observations into intervals and displays their
frequencies or relative frequencies.
5. A sample contains the values 4, 7, 8, 10, and 16. What is the sample mean?
A. 8
B. 8.5
C. 9
D. 10
Rationale: The sample mean is (4 + 7 + 8 + 10 + 16)/5 = 45/5 = 9.
6. Which measure of center is generally least affected by an extremely large or small
observation?
A. Mean
B. Median
C. Range
D. Variance
Rationale: The median depends on the ordered position of observations and is therefore resistant
to extreme values. The mean can be substantially influenced by outliers.
7. For a data set with 12 observations, the sample variance is calculated using which
denominator?
A. 12
B. 11
, C. 13
D. 11 after subtracting the sample mean from each observation
Rationale: The sample variance uses n − 1 degrees of freedom. For n = 12, the denominator is
11.
8. If every observation in a data set is increased by 5, what happens to the sample
variance?
A. It increases by 5.
B. It increases by 25.
C. It remains unchanged.
D. It becomes five times larger.
Rationale: Adding a constant shifts every observation equally but does not change the distances
among observations. Therefore, variance is unchanged.
9. If every observation in a data set is multiplied by 3, the variance is multiplied by:
A. 3
B. 9
C. 6
D. 1/3
Rationale: Variance scales by the square of the multiplication factor. Thus, multiplying
observations by 3 multiplies variance by 3² = 9.
10. A distribution has a long tail extending toward larger values. Which description best
characterizes its shape?
A. Symmetric
B. Left-skewed
C. Uniform
D. Right-skewed
