STAT201 Introduction to Statistics Practice Exam Study Guide
Updated 2026 | Verified Questions and Answers with Detailed
Rationales | Descriptive Statistics, Probability Distributions,
Sampling Methods, Hypothesis Testing, Confidence Intervals, p-
Values, Correlation and Regression Analysis, Data Interpretation,
Normal Distribution, Inferential Statistics Concepts | Complete
Exam Prep Resource for Statistics Students Success
Question 1: Which of the following best describes the purpose of descriptive
statistics?
A. To test hypotheses about population parameters
B. To make predictions about future data points
C. To summarize and describe the main features of a dataset
D. To determine causal relationships between variables
CORRECT ANSWER: C. To summarize and describe the main features of a dataset
RATIONALE : Descriptive statistics involve methods for organizing, summarizing, and
presenting data in a clear and informative way, such as through measures of central
tendency (mean, median) and variability (standard deviation, range), without making
inferences beyond the data.
Question 2: In a standard normal distribution, what is the mean and standard
deviation?
A. Mean = 1, Standard Deviation = 0
B. Mean = 0, Standard Deviation = 1
C. Mean = 1, Standard Deviation = 1
D. Mean = 0, Standard Deviation = 0
CORRECT ANSWER: B. Mean = 0, Standard Deviation = 1
RATIONALE : The standard normal distribution is a special case of the normal
distribution with a mean of 0 and a standard deviation of 1. It is used as a reference
distribution in many statistical procedures.
Question 3: Which measure of central tendency is most affected by extreme
outliers?
A. Median
B. Mode
C. Mean
D. Midrange
CORRECT ANSWER: C. Mean
,RATIONALE : The mean incorporates all values in the dataset, so extreme values
(outliers) can significantly pull it away from the center of the distribution. The median
and mode are more robust to outliers.
Question 4: A Type I error in hypothesis testing occurs when:
A. The null hypothesis is true, but we fail to reject it
B. The alternative hypothesis is false, but we accept it
C. The null hypothesis is false, but we reject it
D. The null hypothesis is true, but we reject it
CORRECT ANSWER: D. The null hypothesis is true, but we reject it
RATIONALE : A Type I error is the incorrect rejection of a true null hypothesis. The
probability of committing a Type I error is denoted by α (alpha), the significance level.
Question 5: What does a p-value represent in hypothesis testing?
A. The probability that the null hypothesis is true
B. The probability of observing a test statistic as extreme or more extreme than the one
observed, assuming the null hypothesis is true
C. The probability that the alternative hypothesis is false
D. The effect size of the observed difference
CORRECT ANSWER: B. The probability of observing a test statistic as extreme or
more extreme than the one observed, assuming the null hypothesis is true
RATIONALE : The p-value quantifies the strength of evidence against the null
hypothesis under the assumption that it is true. A small p-value suggests that the
observed data would be unlikely if the null were correct.
Question 6: Which of the following is a requirement for using the t-distribution
instead of the z-distribution?
A. Population standard deviation is known
B. Sample size is greater than 30
C. Population standard deviation is unknown and estimated from the sample
D. Data must be categorical
CORRECT ANSWER: C. Population standard deviation is unknown and estimated
from the sample
RATIONALE : The t-distribution is used when the population standard deviation is
unknown and must be estimated using the sample standard deviation, especially with
small sample sizes.
Question 7: If two events A and B are independent, which of the following is true?
A. P(A ∩ B) = P(A) + P(B)
B. P(A ∩ B) = P(A) × P(B)
, C. P(A | B) = 0
D. P(A ∪ B) = P(A) × P(B)
CORRECT ANSWER: B. P(A ∩ B) = P(A) × P(B)
RATIONALE : For independent events, the occurrence of one does not affect the
probability of the other. Thus, the joint probability equals the product of their individual
probabilities.
Question 8: What is the interquartile range (IQR)?
A. The difference between the maximum and minimum values
B. The average of the first and third quartiles
C. The range of the middle 50% of the data
D. The square root of the variance
CORRECT ANSWER: C. The range of the middle 50% of the data
RATIONALE : The IQR is calculated as Q3 – Q1, where Q1 is the 25th percentile and Q3
is the 75th percentile. It measures the spread of the central half of the data and is
resistant to outliers.
Question 9: Which sampling method ensures every member of the population has
an equal chance of being selected?
A. Convenience sampling
B. Stratified sampling
C. Simple random sampling
D. Cluster sampling
CORRECT ANSWER: C. Simple random sampling
RATIONALE : In simple random sampling, each individual in the population has an
equal and independent chance of being included in the sample, minimizing selection
bias.
Question 10: A 95% confidence interval for a population mean implies that:
A. There is a 95% probability that the population mean lies within the interval
B. 95% of the sample data fall within the interval
C. If we repeated the sampling process many times, 95% of the resulting intervals would
contain the true population mean
D. The margin of error is 5%
CORRECT ANSWER: C. If we repeated the sampling process many times, 95% of the
resulting intervals would contain the true population mean
RATIONALE : A confidence interval is a frequentist concept; the 95% confidence level
refers to the long-run proportion of intervals that would capture the true parameter, not
the probability for any single interval.
Updated 2026 | Verified Questions and Answers with Detailed
Rationales | Descriptive Statistics, Probability Distributions,
Sampling Methods, Hypothesis Testing, Confidence Intervals, p-
Values, Correlation and Regression Analysis, Data Interpretation,
Normal Distribution, Inferential Statistics Concepts | Complete
Exam Prep Resource for Statistics Students Success
Question 1: Which of the following best describes the purpose of descriptive
statistics?
A. To test hypotheses about population parameters
B. To make predictions about future data points
C. To summarize and describe the main features of a dataset
D. To determine causal relationships between variables
CORRECT ANSWER: C. To summarize and describe the main features of a dataset
RATIONALE : Descriptive statistics involve methods for organizing, summarizing, and
presenting data in a clear and informative way, such as through measures of central
tendency (mean, median) and variability (standard deviation, range), without making
inferences beyond the data.
Question 2: In a standard normal distribution, what is the mean and standard
deviation?
A. Mean = 1, Standard Deviation = 0
B. Mean = 0, Standard Deviation = 1
C. Mean = 1, Standard Deviation = 1
D. Mean = 0, Standard Deviation = 0
CORRECT ANSWER: B. Mean = 0, Standard Deviation = 1
RATIONALE : The standard normal distribution is a special case of the normal
distribution with a mean of 0 and a standard deviation of 1. It is used as a reference
distribution in many statistical procedures.
Question 3: Which measure of central tendency is most affected by extreme
outliers?
A. Median
B. Mode
C. Mean
D. Midrange
CORRECT ANSWER: C. Mean
,RATIONALE : The mean incorporates all values in the dataset, so extreme values
(outliers) can significantly pull it away from the center of the distribution. The median
and mode are more robust to outliers.
Question 4: A Type I error in hypothesis testing occurs when:
A. The null hypothesis is true, but we fail to reject it
B. The alternative hypothesis is false, but we accept it
C. The null hypothesis is false, but we reject it
D. The null hypothesis is true, but we reject it
CORRECT ANSWER: D. The null hypothesis is true, but we reject it
RATIONALE : A Type I error is the incorrect rejection of a true null hypothesis. The
probability of committing a Type I error is denoted by α (alpha), the significance level.
Question 5: What does a p-value represent in hypothesis testing?
A. The probability that the null hypothesis is true
B. The probability of observing a test statistic as extreme or more extreme than the one
observed, assuming the null hypothesis is true
C. The probability that the alternative hypothesis is false
D. The effect size of the observed difference
CORRECT ANSWER: B. The probability of observing a test statistic as extreme or
more extreme than the one observed, assuming the null hypothesis is true
RATIONALE : The p-value quantifies the strength of evidence against the null
hypothesis under the assumption that it is true. A small p-value suggests that the
observed data would be unlikely if the null were correct.
Question 6: Which of the following is a requirement for using the t-distribution
instead of the z-distribution?
A. Population standard deviation is known
B. Sample size is greater than 30
C. Population standard deviation is unknown and estimated from the sample
D. Data must be categorical
CORRECT ANSWER: C. Population standard deviation is unknown and estimated
from the sample
RATIONALE : The t-distribution is used when the population standard deviation is
unknown and must be estimated using the sample standard deviation, especially with
small sample sizes.
Question 7: If two events A and B are independent, which of the following is true?
A. P(A ∩ B) = P(A) + P(B)
B. P(A ∩ B) = P(A) × P(B)
, C. P(A | B) = 0
D. P(A ∪ B) = P(A) × P(B)
CORRECT ANSWER: B. P(A ∩ B) = P(A) × P(B)
RATIONALE : For independent events, the occurrence of one does not affect the
probability of the other. Thus, the joint probability equals the product of their individual
probabilities.
Question 8: What is the interquartile range (IQR)?
A. The difference between the maximum and minimum values
B. The average of the first and third quartiles
C. The range of the middle 50% of the data
D. The square root of the variance
CORRECT ANSWER: C. The range of the middle 50% of the data
RATIONALE : The IQR is calculated as Q3 – Q1, where Q1 is the 25th percentile and Q3
is the 75th percentile. It measures the spread of the central half of the data and is
resistant to outliers.
Question 9: Which sampling method ensures every member of the population has
an equal chance of being selected?
A. Convenience sampling
B. Stratified sampling
C. Simple random sampling
D. Cluster sampling
CORRECT ANSWER: C. Simple random sampling
RATIONALE : In simple random sampling, each individual in the population has an
equal and independent chance of being included in the sample, minimizing selection
bias.
Question 10: A 95% confidence interval for a population mean implies that:
A. There is a 95% probability that the population mean lies within the interval
B. 95% of the sample data fall within the interval
C. If we repeated the sampling process many times, 95% of the resulting intervals would
contain the true population mean
D. The margin of error is 5%
CORRECT ANSWER: C. If we repeated the sampling process many times, 95% of the
resulting intervals would contain the true population mean
RATIONALE : A confidence interval is a frequentist concept; the 95% confidence level
refers to the long-run proportion of intervals that would capture the true parameter, not
the probability for any single interval.
