MATH 110 FINAL EXAM:
INTRODUCTION TO STATISTICS
2026/2027 UPDATE. JUST RELEASED
1. Which of the following describes the ‘Law of Large Numbers’ in the context of probability?
A. A larger sample size will always result in a smaller standard deviation of the population.
B. The sum of a large number of independent random variables will follow a normal
distribution.
C. The mean of a sample is always equal to the population mean if the sample size is greater
than 30.
D. As the number of trials increases, the relative frequency of an event approaches its
theoretical probability.
Answer: D
Conceptual Explanation: The Law of Large Numbers states that as a sample size grows, its
mean gets closer to the average of the whole population (theoretical probability).
2. In a negatively skewed distribution, which of the following relationships is typically true?
A. Mean > Median > Mode
,B. Mean = Median = Mode
C. Mean < Median < Mode
D. Mode < Median < Mean
Answer: C
Conceptual Explanation: In a negatively skewed distribution, the tail is on the left, pulling
the mean down the most, followed by the median, while the mode remains at the peak.
3. If the correlation coefficient (r) between two variables is -0.85, what does this indicate?
A. A weak negative linear relationship
B. A strong negative linear relationship
C. A strong positive linear relationship
D. No linear relationship exists
Answer: B
Conceptual Explanation: An r-value close to -1 indicates a strong negative linear
relationship.
4. Under what condition does the binomial distribution closely approximate the Poisson
distribution?
A. When n is small and p is large
B. When n and p are both very large
, C. When n is large and p is small
D. When n is equal to 1-p
Answer: C
Conceptual Explanation: The Poisson distribution is used as an approximation to the
Binomial when the number of trials n is large and the probability of success p is small
(usually np < 7).
5. A Type II error occurs when:
A. The null hypothesis is rejected when it is true.
B. The alternative hypothesis is accepted when it is false.
C. The null hypothesis is not rejected when it is false.
D. The p-value is less than the alpha level.
Answer: C
Conceptual Explanation: A Type II error (beta) happens when the test fails to reject a
false null hypothesis.
6. What is the primary purpose of the Central Limit Theorem?
A. To ensure that all populations follow a normal distribution.
B. To calculate the exact value of the population standard deviation.
C. To allow the use of normal distribution methods for sample means from non-normal
populations, provided n is large enough.
INTRODUCTION TO STATISTICS
2026/2027 UPDATE. JUST RELEASED
1. Which of the following describes the ‘Law of Large Numbers’ in the context of probability?
A. A larger sample size will always result in a smaller standard deviation of the population.
B. The sum of a large number of independent random variables will follow a normal
distribution.
C. The mean of a sample is always equal to the population mean if the sample size is greater
than 30.
D. As the number of trials increases, the relative frequency of an event approaches its
theoretical probability.
Answer: D
Conceptual Explanation: The Law of Large Numbers states that as a sample size grows, its
mean gets closer to the average of the whole population (theoretical probability).
2. In a negatively skewed distribution, which of the following relationships is typically true?
A. Mean > Median > Mode
,B. Mean = Median = Mode
C. Mean < Median < Mode
D. Mode < Median < Mean
Answer: C
Conceptual Explanation: In a negatively skewed distribution, the tail is on the left, pulling
the mean down the most, followed by the median, while the mode remains at the peak.
3. If the correlation coefficient (r) between two variables is -0.85, what does this indicate?
A. A weak negative linear relationship
B. A strong negative linear relationship
C. A strong positive linear relationship
D. No linear relationship exists
Answer: B
Conceptual Explanation: An r-value close to -1 indicates a strong negative linear
relationship.
4. Under what condition does the binomial distribution closely approximate the Poisson
distribution?
A. When n is small and p is large
B. When n and p are both very large
, C. When n is large and p is small
D. When n is equal to 1-p
Answer: C
Conceptual Explanation: The Poisson distribution is used as an approximation to the
Binomial when the number of trials n is large and the probability of success p is small
(usually np < 7).
5. A Type II error occurs when:
A. The null hypothesis is rejected when it is true.
B. The alternative hypothesis is accepted when it is false.
C. The null hypothesis is not rejected when it is false.
D. The p-value is less than the alpha level.
Answer: C
Conceptual Explanation: A Type II error (beta) happens when the test fails to reject a
false null hypothesis.
6. What is the primary purpose of the Central Limit Theorem?
A. To ensure that all populations follow a normal distribution.
B. To calculate the exact value of the population standard deviation.
C. To allow the use of normal distribution methods for sample means from non-normal
populations, provided n is large enough.
