PCAT Statistics 2 — Questions and Answers
Question 1: A dataset has a mean of 50 and a standard deviation of 10. What is the z-score of a value of 35?
- -1.5 (Correct answer)
- -2.0
- 1.5
- 2.0
Correct answer: -1.5
Z = (35 - 50) / 10 = -15 / 10 = -1.5.
Question 2: Which measure of central tendency is most affected by extreme outliers?
- Mean (Correct answer)
- Median
- Mode
- Midrange
Correct answer: Mean
The mean incorporates all values arithmetically, so extreme outliers pull it significantly.
Question 3: A clinical trial reports a p-value of 0.03. Which conclusion is most appropriate at α = 0.05?
- Reject the null hypothesis (Correct answer)
- Fail to reject the null hypothesis
- Accept the null hypothesis
- The result is clinically significant
Correct answer: Reject the null hypothesis
Since p = 0.03 < α = 0.05, there is sufficient evidence to reject the null hypothesis.
Question 4: In a normal distribution, approximately what percentage of data falls within two standard deviations of the mean?
- 95% (Correct answer)
- 68%
- 99.7%
- 50%
Correct answer: 95%
The empirical rule states that ~95% of data falls within ±2 standard deviations in a normal distribution.
Question 5: A researcher wants to determine if there is a linear relationship between drug dose and response. Which statistical test is most appropriate?
- Pearson correlation (Correct answer)
- Chi-square test
- ANOVA
- Mann-Whitney U test
Correct answer: Pearson correlation
Pearson correlation measures the strength and direction of a linear relationship between two continuous variables.
Question 6: What is the variance of the dataset {2, 4, 4, 4, 5, 5, 7, 9}?
- 4 (Correct answer)
- 2
- 16
- 5
Correct answer: 4
The mean is 5; variance = [(9+1+1+1+0+0+4+16)/8] = 32/8 = 4.
Question 7: A 95% confidence interval for a mean is (12.3, 18.7). What does this mean?
- We are 95% confident the true population mean lies between 12.3 and 18.7 (Correct answer)
- 95% of data points fall between 12.3 and 18.7
- There is a 95% probability the sample mean equals 15.5
- The null hypothesis is rejected at the 5% level
Correct answer: We are 95% confident the true population mean lies between 12.3 and 18.7
A 95% CI means that 95% of intervals constructed this way will contain the true population parameter.
PCAT Statistics 2
A dataset has a mean of 50 and a standard deviation of 10.
What is the z-score of a value of 35?