PCAT Statistics 4 — Questions and Answers
Question 1: A drug study uses a two-tailed t-test with 20 degrees of freedom at α = 0.05. The critical t-value is approximately 2.086. If the calculated t = 2.5, what is the conclusion?
- Reject the null hypothesis (Correct answer)
- Fail to reject the null hypothesis
- Accept the alternative hypothesis directly
- The result is inconclusive
Correct answer: Reject the null hypothesis
Since |t| = 2.5 > 2.086 (critical value), the null hypothesis is rejected.
Question 2: What is the probability of rolling a sum of 7 with two fair six-sided dice?
- 1/6 (Correct answer)
- 1/12
- 1/36
- 7/36
Correct answer: 1/6
There are 6 favorable outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 total, so P = 6/36 = 1/6.
Question 3: A researcher calculates a 90% confidence interval instead of a 95% CI using the same data. How does the width change?
- The interval becomes narrower (Correct answer)
- The interval becomes wider
- The interval width stays the same
- The interval shifts to the right
Correct answer: The interval becomes narrower
Lower confidence levels correspond to smaller critical values, producing narrower confidence intervals.
Question 4: Which statistical test compares proportions between two independent groups?
- Chi-square test of independence (Correct answer)
- Paired t-test
- One-sample t-test
- ANOVA
Correct answer: Chi-square test of independence
The chi-square test of independence compares categorical proportions between two or more independent groups.
Question 5: In hypothesis testing, what does increasing the sample size primarily accomplish?
- Increases statistical power (Correct answer)
- Increases the probability of Type I error
- Widens the confidence interval
- Decreases the significance level
Correct answer: Increases statistical power
Larger samples reduce standard error, making it easier to detect true effects and increasing statistical power.
Question 6: A dataset has values {10, 20, 30, 40, 50}. What is the coefficient of variation (CV)?
- 47.1% (Correct answer)
- 15.8%
- 30%
- 10%
Correct answer: 47.1%
Mean = 30, SD ≈ 15.81; CV = (15.81/30) × 100 ≈ 52.7%, closest to 47.1% among PCAT approximations — SD = √200 ≈ 14.14, CV = 14.14/30 ≈ 47.1%.
Question 7: Which of the following is a non-parametric alternative to the independent samples t-test?
- Mann-Whitney U test (Correct answer)
- ANOVA
- Pearson correlation
- Z-test
Correct answer: Mann-Whitney U test
The Mann-Whitney U test compares two independent groups without assuming normality, making it non-parametric.
PCAT Statistics 4
A drug study uses a two-tailed t-test with 20 degrees of freedom at α = 0.05.
The critical t-value is approximately 2.086.
If the calculated t = 2.5, what is the conclusion?