STAT 200 ADVANCED STATISTICS
COMPREHENSIVE EXAM QUESTIONS
AND ANSWERS
1. In a hypothesis test, if the null hypothesis is rejected at the 0.05 significance level, which of
the following must be true?
A. The p-value is greater than 0.05.
B. The null hypothesis is definitely false.
C. A 95% confidence interval for the parameter would not contain the null value.
D. The probability of a Type II error is 0.05.
Answer: C
Conceptual Explanation: Rejecting the null hypothesis at alpha = 0.05 is mathematically
equivalent to the null value falling outside the corresponding 95% confidence interval.
2. Which of the following best describes a Type II error?
A. Failing to reject a false null hypothesis.
B. Rejecting a true null hypothesis.
C. Rejecting a false null hypothesis.
,D. Failing to reject a true null hypothesis.
Answer: A
Conceptual Explanation: A Type II error (beta) occurs when the test fails to reject a null
hypothesis that is actually false in reality.
3. A researcher calculates a correlation coefficient of r = -0.85 between study hours and exam
anxiety. What does this indicate?
A. Study hours cause a decrease in anxiety.
B. There is a strong negative linear relationship.
C. There is a strong positive linear relationship.
D. 85% of the variance in anxiety is explained by study hours.
Answer: B
Conceptual Explanation: An r value of -0.85 indicates a strong negative linear
relationship. Correlation does not imply causation, and r-squared (not r) explains variance.
4. According to the Central Limit Theorem, the sampling distribution of the sample mean will
be approximately normal if:
A. The sample size is sufficiently large (usually n >= 30).
B. The population distribution is perfectly normal regardless of sample size.
C. The population standard deviation is known.
D. The data is collected using a convenience sample.
, Answer: A
Conceptual Explanation: The CLT states that for a large enough sample size (typically n
>= 30), the sampling distribution of the mean is approximately normal, regardless of the
population’s shape.
5. In a simple linear regression model, what does the coefficient of determination (R-squared)
represent?
A. The slope of the regression line.
B. The proportion of variation in the dependent variable explained by the independent
variable.
C. The probability that the null hypothesis is true.
D. The average error of the predictions.
Answer: B
Conceptual Explanation: R-squared measures the proportion of the total variation in the
Y variable that is accounted for by the regression model involving the X variable.
6. Which measure of central tendency is most sensitive to extreme outliers?
A. Median
B. Mode
C. Interquartile Range
D. Mean
COMPREHENSIVE EXAM QUESTIONS
AND ANSWERS
1. In a hypothesis test, if the null hypothesis is rejected at the 0.05 significance level, which of
the following must be true?
A. The p-value is greater than 0.05.
B. The null hypothesis is definitely false.
C. A 95% confidence interval for the parameter would not contain the null value.
D. The probability of a Type II error is 0.05.
Answer: C
Conceptual Explanation: Rejecting the null hypothesis at alpha = 0.05 is mathematically
equivalent to the null value falling outside the corresponding 95% confidence interval.
2. Which of the following best describes a Type II error?
A. Failing to reject a false null hypothesis.
B. Rejecting a true null hypothesis.
C. Rejecting a false null hypothesis.
,D. Failing to reject a true null hypothesis.
Answer: A
Conceptual Explanation: A Type II error (beta) occurs when the test fails to reject a null
hypothesis that is actually false in reality.
3. A researcher calculates a correlation coefficient of r = -0.85 between study hours and exam
anxiety. What does this indicate?
A. Study hours cause a decrease in anxiety.
B. There is a strong negative linear relationship.
C. There is a strong positive linear relationship.
D. 85% of the variance in anxiety is explained by study hours.
Answer: B
Conceptual Explanation: An r value of -0.85 indicates a strong negative linear
relationship. Correlation does not imply causation, and r-squared (not r) explains variance.
4. According to the Central Limit Theorem, the sampling distribution of the sample mean will
be approximately normal if:
A. The sample size is sufficiently large (usually n >= 30).
B. The population distribution is perfectly normal regardless of sample size.
C. The population standard deviation is known.
D. The data is collected using a convenience sample.
, Answer: A
Conceptual Explanation: The CLT states that for a large enough sample size (typically n
>= 30), the sampling distribution of the mean is approximately normal, regardless of the
population’s shape.
5. In a simple linear regression model, what does the coefficient of determination (R-squared)
represent?
A. The slope of the regression line.
B. The proportion of variation in the dependent variable explained by the independent
variable.
C. The probability that the null hypothesis is true.
D. The average error of the predictions.
Answer: B
Conceptual Explanation: R-squared measures the proportion of the total variation in the
Y variable that is accounted for by the regression model involving the X variable.
6. Which measure of central tendency is most sensitive to extreme outliers?
A. Median
B. Mode
C. Interquartile Range
D. Mean
