MATH 225N STATISTICAL REASONING
COMPREHENSIVE FINAL EXAM
QUESTIONS AND VERIFIED ANSWERS
|100% CORRECT| GRADE A+
1. A researcher wants to compare the effectiveness of three different pain relief medications.
Which statistical test is most appropriate for comparing the means of more than two groups?
A. Independent samples t-test
B. Chi-square test of independence
C. Linear regression analysis
D. One-way ANOVA
Answer: D
Conceptual Explanation: One-way ANOVA (Analysis of Variance) is used to determine
whether there are any statistically significant differences between the means of three or
more independent groups.
2. If a researcher decreases the level of significance (alpha) from 0.05 to 0.01, what happens
to the probability of committing a Type II error, assuming all other factors remain constant?
A. It increases
B. It decreases
,C. It remains the same
D. It becomes zero
Answer: A
Conceptual Explanation: There is an inverse relationship between Alpha (Type I error)
and Beta (Type II error). Decreasing the risk of a Type I error by lowering alpha increases
the risk of a Type II error.
3. In a normal distribution, approximately what percentage of data points fall within two
standard deviations of the mean?
A. 95%
B. 99.7%
C. 50%
D. 68%
Answer: A
Conceptual Explanation: According to the Empirical Rule (68-95-99.7 rule),
approximately 95% of data in a normal distribution falls within two standard deviations of
the mean.
4. Which of the following correlation coefficients indicates the strongest linear relationship
between two variables?
A. 0.85
, B. -0.40
C. 0.05
D. -0.92
Answer: D
Conceptual Explanation: The strength of a correlation is determined by its absolute value.
|-0.92| is 0.92, which is closer to 1 than 0.85, representing a stronger relationship.
5. What is the primary purpose of the Central Limit Theorem in statistics?
A. To describe the distribution of the sample mean as the sample size becomes large
B. To prove that all populations are normally distributed
C. To calculate the exact mean of a population
D. To determine if a sample is biased
Answer: A
Conceptual Explanation: The Central Limit Theorem states that as the sample size
increases, the sampling distribution of the sample mean approaches a normal distribution,
regardless of the population’s distribution shape.
6. A survey asks participants to rate their satisfaction on a scale of ‘Very Dissatisfied,
Dissatisfied, Neutral, Satisfied, Very Satisfied’. What level of measurement is this data?
A. Nominal
B. Ordinal
COMPREHENSIVE FINAL EXAM
QUESTIONS AND VERIFIED ANSWERS
|100% CORRECT| GRADE A+
1. A researcher wants to compare the effectiveness of three different pain relief medications.
Which statistical test is most appropriate for comparing the means of more than two groups?
A. Independent samples t-test
B. Chi-square test of independence
C. Linear regression analysis
D. One-way ANOVA
Answer: D
Conceptual Explanation: One-way ANOVA (Analysis of Variance) is used to determine
whether there are any statistically significant differences between the means of three or
more independent groups.
2. If a researcher decreases the level of significance (alpha) from 0.05 to 0.01, what happens
to the probability of committing a Type II error, assuming all other factors remain constant?
A. It increases
B. It decreases
,C. It remains the same
D. It becomes zero
Answer: A
Conceptual Explanation: There is an inverse relationship between Alpha (Type I error)
and Beta (Type II error). Decreasing the risk of a Type I error by lowering alpha increases
the risk of a Type II error.
3. In a normal distribution, approximately what percentage of data points fall within two
standard deviations of the mean?
A. 95%
B. 99.7%
C. 50%
D. 68%
Answer: A
Conceptual Explanation: According to the Empirical Rule (68-95-99.7 rule),
approximately 95% of data in a normal distribution falls within two standard deviations of
the mean.
4. Which of the following correlation coefficients indicates the strongest linear relationship
between two variables?
A. 0.85
, B. -0.40
C. 0.05
D. -0.92
Answer: D
Conceptual Explanation: The strength of a correlation is determined by its absolute value.
|-0.92| is 0.92, which is closer to 1 than 0.85, representing a stronger relationship.
5. What is the primary purpose of the Central Limit Theorem in statistics?
A. To describe the distribution of the sample mean as the sample size becomes large
B. To prove that all populations are normally distributed
C. To calculate the exact mean of a population
D. To determine if a sample is biased
Answer: A
Conceptual Explanation: The Central Limit Theorem states that as the sample size
increases, the sampling distribution of the sample mean approaches a normal distribution,
regardless of the population’s distribution shape.
6. A survey asks participants to rate their satisfaction on a scale of ‘Very Dissatisfied,
Dissatisfied, Neutral, Satisfied, Very Satisfied’. What level of measurement is this data?
A. Nominal
B. Ordinal
