, Question 1
A screening test for a rare disease has sensitivity 0.95 and specificity 0.90. In a
population where prevalence is 0.01, what is the positive predictive value
(PPV) closest to?
A. 0.088
B. 0.500
C. 0.905
D. 0.950
Correct Answer: A - 0.088
RATIONALE
PPV = (0.95×0.01)/[(0.95×0.01)+(0.10×0.99)] = 0.0095/0.1085
0.0876. Distractor B reflects confusion with 1specificity; C inverts the
formula; D mistakenly equates PPV with sensitivity. This illustrates
the base-rate fallacy.
Question 2
A simple random sample of 64 observations yields a sample mean of 52 and
sample standard deviation of 8. Which statement about the 95% confidence
interval for the population mean is correct?
A. It is 52 ± 1.96(8/64), valid because n is large enough for the CLT.
B. It is 52 ± 2.00(8/64), using t with 63 df, and is wider than the
z-interval.
C. It is 52 ± 1.96(8/8), but only if the population is exactly normal.
D. It cannot be constructed because the population standard deviation is
unknown.
Correct Answer: B - It is 52 ± 2.00(8/64), using t with 63 df, and is
wider than the z-interval.
Page 2
, RATIONALE
With unknown , the t-distribution with n1=63 df is appropriate;
t_{0.025,63}2.00, yielding a slightly wider interval than the z-interval.
A is a common but technically incorrect approximation; C
miscalculates the standard error; D is false because s estimates .
Question 3
A regression of salary on years of experience and education yields VIF values
of 12 for experience and 11 for education. What is the most defensible
interpretation and remedy?
A. Multicollinearity is absent; proceed with interpretation of individual
coefficients.
B. Multicollinearity is severe; coefficients are unstable, so consider
dropping one predictor or using ridge regression.
C. Heteroscedasticity is present; apply weighted least squares.
D. The model has omitted variable bias; add interaction terms.
Correct Answer: B - Multicollinearity is severe; coefficients are
unstable, so consider dropping one predictor or using ridge
regression.
RATIONALE
VIF > 10 signals serious multicollinearity, inflating standard errors
and destabilizing coefficients. A misreads the threshold; C confuses
VIF with heteroscedasticity diagnostics; D addresses a different
assumption violation.
Question 4
An ANOVA comparing four group means yields F(3, 36) = 5.20, p = 0.004.
Which follow-up procedure best controls the familywise error rate while
maintaining power?
A. Perform all six pairwise t-tests at = 0.05.
Page 3
A screening test for a rare disease has sensitivity 0.95 and specificity 0.90. In a
population where prevalence is 0.01, what is the positive predictive value
(PPV) closest to?
A. 0.088
B. 0.500
C. 0.905
D. 0.950
Correct Answer: A - 0.088
RATIONALE
PPV = (0.95×0.01)/[(0.95×0.01)+(0.10×0.99)] = 0.0095/0.1085
0.0876. Distractor B reflects confusion with 1specificity; C inverts the
formula; D mistakenly equates PPV with sensitivity. This illustrates
the base-rate fallacy.
Question 2
A simple random sample of 64 observations yields a sample mean of 52 and
sample standard deviation of 8. Which statement about the 95% confidence
interval for the population mean is correct?
A. It is 52 ± 1.96(8/64), valid because n is large enough for the CLT.
B. It is 52 ± 2.00(8/64), using t with 63 df, and is wider than the
z-interval.
C. It is 52 ± 1.96(8/8), but only if the population is exactly normal.
D. It cannot be constructed because the population standard deviation is
unknown.
Correct Answer: B - It is 52 ± 2.00(8/64), using t with 63 df, and is
wider than the z-interval.
Page 2
, RATIONALE
With unknown , the t-distribution with n1=63 df is appropriate;
t_{0.025,63}2.00, yielding a slightly wider interval than the z-interval.
A is a common but technically incorrect approximation; C
miscalculates the standard error; D is false because s estimates .
Question 3
A regression of salary on years of experience and education yields VIF values
of 12 for experience and 11 for education. What is the most defensible
interpretation and remedy?
A. Multicollinearity is absent; proceed with interpretation of individual
coefficients.
B. Multicollinearity is severe; coefficients are unstable, so consider
dropping one predictor or using ridge regression.
C. Heteroscedasticity is present; apply weighted least squares.
D. The model has omitted variable bias; add interaction terms.
Correct Answer: B - Multicollinearity is severe; coefficients are
unstable, so consider dropping one predictor or using ridge
regression.
RATIONALE
VIF > 10 signals serious multicollinearity, inflating standard errors
and destabilizing coefficients. A misreads the threshold; C confuses
VIF with heteroscedasticity diagnostics; D addresses a different
assumption violation.
Question 4
An ANOVA comparing four group means yields F(3, 36) = 5.20, p = 0.004.
Which follow-up procedure best controls the familywise error rate while
maintaining power?
A. Perform all six pairwise t-tests at = 0.05.
Page 3
