STAT 200: COMPREHENSIVE
STATISTICS ASSESSMENT (2026/2027)
QUESTIONS AND ANSWERS
1. Which of the following best describes a Type II error in hypothesis testing?
A. Rejecting a true null hypothesis
B. Rejecting a false null hypothesis
C. Failing to reject a false null hypothesis
D. Failing to reject a true null hypothesis
Answer: C
Conceptual Explanation: A Type II error occurs when the null hypothesis is false, but the
test fails to reject it. This is often denoted by the Greek letter beta.
2. In a simple linear regression model, what does the coefficient of determination (R-squared)
represent?
A. The proportion of variance in the dependent variable explained by the independent
variable
B. The slope of the regression line
,C. The correlation between the independent and dependent variables
D. The standard error of the estimate
Answer: A
Conceptual Explanation: R-squared measures the percentage of the response variable
variation that is explained by a linear model.
3. According to the Central Limit Theorem, the sampling distribution of the sample mean will
be approximately normal if:
A. The sample size is large, typically n > 30
B. The population distribution is skewed and the sample size is small
C. The population is finite
D. The data is qualitative
Answer: A
Conceptual Explanation: The Central Limit Theorem states that for a large enough sample
size (n > 30), the distribution of sample means will be approximately normal regardless of
the population shape.
4. If the p-value of a test is 0.03 and the significance level (alpha) is 0.05, what is the
appropriate conclusion?
A. Fail to reject the null hypothesis
B. The test is inconclusive
, C. Accept the null hypothesis
D. Reject the null hypothesis
Answer: D
Conceptual Explanation: If the p-value is less than or equal to alpha, the results are
statistically significant, and we reject the null hypothesis.
5. What is the primary difference between a parameter and a statistic?
A. A parameter describes a sample, while a statistic describes a population
B. Statistics are always more accurate than parameters
C. A parameter is a fixed value describing a population, while a statistic is calculated from a
sample
D. Parameters are only used in descriptive statistics
Answer: C
Conceptual Explanation: Parameters are numerical values that summarize data for an
entire population, whereas statistics summarize data from a sample.
6. A researcher uses a sample of 100 students and calculates a 95% confidence interval for the
mean GPA. If they increase the sample size to 400 while keeping the same confidence level,
the width of the interval will:
A. Increase
B. Decrease by half
STATISTICS ASSESSMENT (2026/2027)
QUESTIONS AND ANSWERS
1. Which of the following best describes a Type II error in hypothesis testing?
A. Rejecting a true null hypothesis
B. Rejecting a false null hypothesis
C. Failing to reject a false null hypothesis
D. Failing to reject a true null hypothesis
Answer: C
Conceptual Explanation: A Type II error occurs when the null hypothesis is false, but the
test fails to reject it. This is often denoted by the Greek letter beta.
2. In a simple linear regression model, what does the coefficient of determination (R-squared)
represent?
A. The proportion of variance in the dependent variable explained by the independent
variable
B. The slope of the regression line
,C. The correlation between the independent and dependent variables
D. The standard error of the estimate
Answer: A
Conceptual Explanation: R-squared measures the percentage of the response variable
variation that is explained by a linear model.
3. According to the Central Limit Theorem, the sampling distribution of the sample mean will
be approximately normal if:
A. The sample size is large, typically n > 30
B. The population distribution is skewed and the sample size is small
C. The population is finite
D. The data is qualitative
Answer: A
Conceptual Explanation: The Central Limit Theorem states that for a large enough sample
size (n > 30), the distribution of sample means will be approximately normal regardless of
the population shape.
4. If the p-value of a test is 0.03 and the significance level (alpha) is 0.05, what is the
appropriate conclusion?
A. Fail to reject the null hypothesis
B. The test is inconclusive
, C. Accept the null hypothesis
D. Reject the null hypothesis
Answer: D
Conceptual Explanation: If the p-value is less than or equal to alpha, the results are
statistically significant, and we reject the null hypothesis.
5. What is the primary difference between a parameter and a statistic?
A. A parameter describes a sample, while a statistic describes a population
B. Statistics are always more accurate than parameters
C. A parameter is a fixed value describing a population, while a statistic is calculated from a
sample
D. Parameters are only used in descriptive statistics
Answer: C
Conceptual Explanation: Parameters are numerical values that summarize data for an
entire population, whereas statistics summarize data from a sample.
6. A researcher uses a sample of 100 students and calculates a 95% confidence interval for the
mean GPA. If they increase the sample size to 400 while keeping the same confidence level,
the width of the interval will:
A. Increase
B. Decrease by half
