STRAIGHTERLINE INTRODUCTION TO
STATISTICS ADVANCED EXAM
QUESTIONS WITH VERIFIED ANSWERS
1. Which of the following measures of central tendency is most sensitive to extreme outliers
in a dataset?
A. The median
B. The mode
C. The mean
D. The interquartile range
Answer: C
Conceptual Explanation: The arithmetic mean uses every value in the dataset in its
calculation, making it heavily influenced by extremely high or low outliers.
2. In a positively skewed distribution, what is the typical relationship between the mean,
median, and mode?
A. Mean < Median < Mode
B. Mode < Median < Mean
C. Mean = Median = Mode
,D. Median < Mode < Mean
Answer: B
Conceptual Explanation: In a positively skewed distribution, the extreme values pull the
mean to the right, followed by the median, with the mode remaining at the peak.
3. If two events A and B are mutually exclusive, what is P(A and B)?
A. 1
B. 0.5
C. P(A) * P(B)
D. 0
Answer: D
Conceptual Explanation: Mutually exclusive events cannot occur at the same time,
meaning the probability of both occurring simultaneously is zero.
4. What does the Central Limit Theorem state about the sampling distribution of the sample
mean?
A. It is always uniform if the population is skewed.
B. It only applies when the population size is less than 30.
C. It has a smaller standard deviation than the population standard deviation.
D. It becomes approximately normal as the sample size increases, regardless of the
population distribution.
, Answer: D
Conceptual Explanation: The Central Limit Theorem guarantees that for a sufficiently
large sample size (usually n >= 30), the sampling distribution of the mean will be
approximately normally distributed.
5. When conducting a hypothesis test, a Type I error occurs when:
A. You reject a false null hypothesis
B. You fail to reject a false null hypothesis
C. You reject a true null hypothesis
D. You fail to reject a true null hypothesis
Answer: C
Conceptual Explanation: A Type I error is a false positive, meaning you reject the null
hypothesis when it is actually true.
6. Which of the following describes a Type II error?
A. Failing to reject a false null hypothesis
B. Rejecting a true null hypothesis
C. Accepting the alternative hypothesis when it is false
D. Failing to reject a true alternative hypothesis
Answer: A
STATISTICS ADVANCED EXAM
QUESTIONS WITH VERIFIED ANSWERS
1. Which of the following measures of central tendency is most sensitive to extreme outliers
in a dataset?
A. The median
B. The mode
C. The mean
D. The interquartile range
Answer: C
Conceptual Explanation: The arithmetic mean uses every value in the dataset in its
calculation, making it heavily influenced by extremely high or low outliers.
2. In a positively skewed distribution, what is the typical relationship between the mean,
median, and mode?
A. Mean < Median < Mode
B. Mode < Median < Mean
C. Mean = Median = Mode
,D. Median < Mode < Mean
Answer: B
Conceptual Explanation: In a positively skewed distribution, the extreme values pull the
mean to the right, followed by the median, with the mode remaining at the peak.
3. If two events A and B are mutually exclusive, what is P(A and B)?
A. 1
B. 0.5
C. P(A) * P(B)
D. 0
Answer: D
Conceptual Explanation: Mutually exclusive events cannot occur at the same time,
meaning the probability of both occurring simultaneously is zero.
4. What does the Central Limit Theorem state about the sampling distribution of the sample
mean?
A. It is always uniform if the population is skewed.
B. It only applies when the population size is less than 30.
C. It has a smaller standard deviation than the population standard deviation.
D. It becomes approximately normal as the sample size increases, regardless of the
population distribution.
, Answer: D
Conceptual Explanation: The Central Limit Theorem guarantees that for a sufficiently
large sample size (usually n >= 30), the sampling distribution of the mean will be
approximately normally distributed.
5. When conducting a hypothesis test, a Type I error occurs when:
A. You reject a false null hypothesis
B. You fail to reject a false null hypothesis
C. You reject a true null hypothesis
D. You fail to reject a true null hypothesis
Answer: C
Conceptual Explanation: A Type I error is a false positive, meaning you reject the null
hypothesis when it is actually true.
6. Which of the following describes a Type II error?
A. Failing to reject a false null hypothesis
B. Rejecting a true null hypothesis
C. Accepting the alternative hypothesis when it is false
D. Failing to reject a true alternative hypothesis
Answer: A
