STAT 200 INTRODUCTORY STATISTICS
COMPREHENSIVE EXAM PREP
QUESTIONS AND ANSWERS
1. A researcher divides a population into separate groups called strata and then takes a
proportional random sample from each group. Which sampling method is being used?
A. Stratified Sampling
B. Systematic Sampling
C. Cluster Sampling
D. Convenience Sampling
Answer: A
Conceptual Explanation: Stratified sampling involves dividing the population into
subpopulations (strata) and sampling from each to ensure representation.
2. Which of the following describes a Type I error in hypothesis testing?
A. Rejecting a true null hypothesis
B. Failing to reject a false null hypothesis
C. Rejecting a true alternative hypothesis
,D. Failing to reject a true null hypothesis
Answer: A
Conceptual Explanation: A Type I error occurs when the null hypothesis is actually true,
but we mistakenly reject it (a ‘false positive’).
3. If a distribution is strongly skewed to the right, which of the following is typically true?
A. The median is greater than the mean
B. The mean is greater than the median
C. The mean and median are equal
D. The mode is greater than the mean
Answer: B
Conceptual Explanation: In right-skewed distributions, the long tail on the right pulls the
mean toward the higher values, making it larger than the median.
4. What is the probability of an event that is certain to occur?
A. 0
B. 1
C. 0.5
D. Infinity
Answer: B
, Conceptual Explanation: Probability values range from 0 (impossible) to 1 (certain).
5. The Central Limit Theorem states that as the sample size increases, the distribution of the
sample mean approaches:
A. A binomial distribution
B. A normal distribution
C. A uniform distribution
D. A skewed distribution
Answer: B
Conceptual Explanation: The Central Limit Theorem ensures that the sampling
distribution of the mean becomes approximately normal as n increases, regardless of the
population shape.
6. A Z-score of -2.5 indicates that the data point is:
A. 2.5 units below the mean
B. 2.5 standard deviations above the mean
C. 2.5 percentiles below the mean
D. 2.5 standard deviations below the mean
Answer: D
Conceptual Explanation: A Z-score represents the number of standard deviations a value
is from the mean; negative indicates it is below the mean.
COMPREHENSIVE EXAM PREP
QUESTIONS AND ANSWERS
1. A researcher divides a population into separate groups called strata and then takes a
proportional random sample from each group. Which sampling method is being used?
A. Stratified Sampling
B. Systematic Sampling
C. Cluster Sampling
D. Convenience Sampling
Answer: A
Conceptual Explanation: Stratified sampling involves dividing the population into
subpopulations (strata) and sampling from each to ensure representation.
2. Which of the following describes a Type I error in hypothesis testing?
A. Rejecting a true null hypothesis
B. Failing to reject a false null hypothesis
C. Rejecting a true alternative hypothesis
,D. Failing to reject a true null hypothesis
Answer: A
Conceptual Explanation: A Type I error occurs when the null hypothesis is actually true,
but we mistakenly reject it (a ‘false positive’).
3. If a distribution is strongly skewed to the right, which of the following is typically true?
A. The median is greater than the mean
B. The mean is greater than the median
C. The mean and median are equal
D. The mode is greater than the mean
Answer: B
Conceptual Explanation: In right-skewed distributions, the long tail on the right pulls the
mean toward the higher values, making it larger than the median.
4. What is the probability of an event that is certain to occur?
A. 0
B. 1
C. 0.5
D. Infinity
Answer: B
, Conceptual Explanation: Probability values range from 0 (impossible) to 1 (certain).
5. The Central Limit Theorem states that as the sample size increases, the distribution of the
sample mean approaches:
A. A binomial distribution
B. A normal distribution
C. A uniform distribution
D. A skewed distribution
Answer: B
Conceptual Explanation: The Central Limit Theorem ensures that the sampling
distribution of the mean becomes approximately normal as n increases, regardless of the
population shape.
6. A Z-score of -2.5 indicates that the data point is:
A. 2.5 units below the mean
B. 2.5 standard deviations above the mean
C. 2.5 percentiles below the mean
D. 2.5 standard deviations below the mean
Answer: D
Conceptual Explanation: A Z-score represents the number of standard deviations a value
is from the mean; negative indicates it is below the mean.
