MODERN MATHEMATICAL STATISTICS WITH APPLICATIONS 3RD
EDITION BY JAY L. DEVORE, KENNETH N. BERK, AND MATTHEW A.
CARLTON COMPREHENSIVE EXAM BANK |QUESTIONS WITH VERIFIED
ANSWERS AND DETAILED RATIONALES
TABLE OF CONTENTS
Chapter 1: Overview and Descriptive Statistics (Questions 1-25)
Chapter 2: Probability (Questions 26-50)
Chapter 3: Discrete Random Variables (Questions 51-75)
Chapter 4: Continuous Random Variables (Questions 76-95)
Chapter 5: Joint Probability Distributions (Questions 96-105)
Chapter 6: Sampling Distributions (Questions 106-120)
Chapter 7: Point Estimation (Questions 121-135)
Chapter 8: Statistical Intervals (Questions 136-150)
Chapter 9: Hypothesis Testing (Questions 151-165)
Chapter 10: Two-Sample Inferences (Questions 166-175)
Chapter 11: ANOVA (Questions 176-185)
Chapter 12: Regression and Correlation (Questions 186-195)
Chapter 13: Chi-Squared Tests (Questions 196-200)
CHAPTER 1: OVERVIEW AND DESCRIPTIVE STATISTICS
QUESTION 1
In a sample of 100 phones, what is the chance that more than 20 need service
while under warranty?
This type of question represents which statistical approach?
A. Descriptive statistics
B. Probability
C. Statistical inference
D. Data collection
ANSWER: B
RATIONALE: This is a probability question because it asks "what are the chances"
of a specific future event occurring based on a known or assumed model.
Descriptive statistics would summarize existing data, while statistical inference
would draw conclusions about a population from a sample.
QUESTION 2
1
,Which of the following is a concrete population?
A. All grade point averages for University of California students
B. All possible tensile strengths of a new alloy
C. All possible times a battery can power a specific laptop
D. All possible values of the price of a randomly selected share of stock
ANSWER: A
RATIONALE: A concrete population exists in a finite, identifiable form. The GPAs of
UC students can be located in university records. Options B, C, and D describe
conceptual or hypothetical populations that represent infinite possible
measurements.
QUESTION 3
Which of the following is NOT one of the seven major components of the
investigative process?
A. Determine the objective and define the population
B. Collect data
C. Apply descriptive statistics
D. Use inferential statistics
ANSWER: E (All of the above ARE components)
RATIONALE: All four options are indeed among the seven major components of
the statistical investigative process. The others include designing the study,
analyzing data, and drawing conclusions.
QUESTION 4
A characteristic that varies from one individual to another is called a:
A. Parameter
B. Statistic
C. Variable
D. Constant
ANSWER: C
RATIONALE: By definition, a variable is a characteristic that takes on different
values for different individuals. A parameter describes a population, a statistic
describes a sample, and a constant does not vary.
2
,QUESTION 5
Which scale of measurement has a true zero point?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
ANSWER: D
RATIONALE: The ratio scale has a true zero point that indicates the absence of the
quantity being measured. Examples include height, weight, and time. The interval
scale (like temperature in Fahrenheit) has no true zero.
QUESTION 6
The number of defective items in a production lot is an example of:
A. Categorical data
B. Continuous numerical data
C. Discrete numerical data
D. Ordinal data
ANSWER: C
RATIONALE: The count of defective items takes on whole number values (0, 1, 2,
...) and is therefore discrete numerical data. It is not categorical because the
numbers have meaningful quantitative value.
QUESTION 7
A bar chart is most appropriate for displaying:
A. Categorical data
B. Continuous numerical data
C. Time series data
D. Bivariate numerical data
ANSWER: A
RATIONALE: Bar charts are designed for categorical data where each bar
represents a category. Histograms are used for continuous numerical data, and
time series plots are used for data over time.
3
, QUESTION 8
The median of the data set {2, 4, 7, 9, 11} is:
A. 6.6
B. 7
C. 8
D. 9
ANSWER: B
RATIONALE: For an odd number of observations (n=5), the median is the middle
value when sorted. The middle value is the 3rd observation, which is 7.
QUESTION 9
The mean of a distribution is 50 and the median is 45. The distribution is:
A. Symmetric
B. Positively skewed
C. Negatively skewed
D. Cannot be determined
ANSWER: B
RATIONALE: In a positively skewed (right-skewed) distribution, the mean is pulled
toward the right tail and is greater than the median. Since 50 > 45, the
distribution is positively skewed.
QUESTION 10
Which measure of spread is least affected by outliers?
A. Range
B. Variance
C. Standard deviation
D. Interquartile range (IQR)
ANSWER: D
RATIONALE: The IQR is based on the 25th and 75th percentiles and is resistant to
outliers. The range, variance, and standard deviation are all sensitive to extreme
values.
4
EDITION BY JAY L. DEVORE, KENNETH N. BERK, AND MATTHEW A.
CARLTON COMPREHENSIVE EXAM BANK |QUESTIONS WITH VERIFIED
ANSWERS AND DETAILED RATIONALES
TABLE OF CONTENTS
Chapter 1: Overview and Descriptive Statistics (Questions 1-25)
Chapter 2: Probability (Questions 26-50)
Chapter 3: Discrete Random Variables (Questions 51-75)
Chapter 4: Continuous Random Variables (Questions 76-95)
Chapter 5: Joint Probability Distributions (Questions 96-105)
Chapter 6: Sampling Distributions (Questions 106-120)
Chapter 7: Point Estimation (Questions 121-135)
Chapter 8: Statistical Intervals (Questions 136-150)
Chapter 9: Hypothesis Testing (Questions 151-165)
Chapter 10: Two-Sample Inferences (Questions 166-175)
Chapter 11: ANOVA (Questions 176-185)
Chapter 12: Regression and Correlation (Questions 186-195)
Chapter 13: Chi-Squared Tests (Questions 196-200)
CHAPTER 1: OVERVIEW AND DESCRIPTIVE STATISTICS
QUESTION 1
In a sample of 100 phones, what is the chance that more than 20 need service
while under warranty?
This type of question represents which statistical approach?
A. Descriptive statistics
B. Probability
C. Statistical inference
D. Data collection
ANSWER: B
RATIONALE: This is a probability question because it asks "what are the chances"
of a specific future event occurring based on a known or assumed model.
Descriptive statistics would summarize existing data, while statistical inference
would draw conclusions about a population from a sample.
QUESTION 2
1
,Which of the following is a concrete population?
A. All grade point averages for University of California students
B. All possible tensile strengths of a new alloy
C. All possible times a battery can power a specific laptop
D. All possible values of the price of a randomly selected share of stock
ANSWER: A
RATIONALE: A concrete population exists in a finite, identifiable form. The GPAs of
UC students can be located in university records. Options B, C, and D describe
conceptual or hypothetical populations that represent infinite possible
measurements.
QUESTION 3
Which of the following is NOT one of the seven major components of the
investigative process?
A. Determine the objective and define the population
B. Collect data
C. Apply descriptive statistics
D. Use inferential statistics
ANSWER: E (All of the above ARE components)
RATIONALE: All four options are indeed among the seven major components of
the statistical investigative process. The others include designing the study,
analyzing data, and drawing conclusions.
QUESTION 4
A characteristic that varies from one individual to another is called a:
A. Parameter
B. Statistic
C. Variable
D. Constant
ANSWER: C
RATIONALE: By definition, a variable is a characteristic that takes on different
values for different individuals. A parameter describes a population, a statistic
describes a sample, and a constant does not vary.
2
,QUESTION 5
Which scale of measurement has a true zero point?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
ANSWER: D
RATIONALE: The ratio scale has a true zero point that indicates the absence of the
quantity being measured. Examples include height, weight, and time. The interval
scale (like temperature in Fahrenheit) has no true zero.
QUESTION 6
The number of defective items in a production lot is an example of:
A. Categorical data
B. Continuous numerical data
C. Discrete numerical data
D. Ordinal data
ANSWER: C
RATIONALE: The count of defective items takes on whole number values (0, 1, 2,
...) and is therefore discrete numerical data. It is not categorical because the
numbers have meaningful quantitative value.
QUESTION 7
A bar chart is most appropriate for displaying:
A. Categorical data
B. Continuous numerical data
C. Time series data
D. Bivariate numerical data
ANSWER: A
RATIONALE: Bar charts are designed for categorical data where each bar
represents a category. Histograms are used for continuous numerical data, and
time series plots are used for data over time.
3
, QUESTION 8
The median of the data set {2, 4, 7, 9, 11} is:
A. 6.6
B. 7
C. 8
D. 9
ANSWER: B
RATIONALE: For an odd number of observations (n=5), the median is the middle
value when sorted. The middle value is the 3rd observation, which is 7.
QUESTION 9
The mean of a distribution is 50 and the median is 45. The distribution is:
A. Symmetric
B. Positively skewed
C. Negatively skewed
D. Cannot be determined
ANSWER: B
RATIONALE: In a positively skewed (right-skewed) distribution, the mean is pulled
toward the right tail and is greater than the median. Since 50 > 45, the
distribution is positively skewed.
QUESTION 10
Which measure of spread is least affected by outliers?
A. Range
B. Variance
C. Standard deviation
D. Interquartile range (IQR)
ANSWER: D
RATIONALE: The IQR is based on the 25th and 75th percentiles and is resistant to
outliers. The range, variance, and standard deviation are all sensitive to extreme
values.
4
