PCAT Statistics 3 — Questions and Answers
Question 1: Which of the following best describes a Type II error?
- Failing to reject a false null hypothesis (Correct answer)
- Rejecting a true null hypothesis
- Accepting a true null hypothesis
- Rejecting a false null hypothesis
Correct answer: Failing to reject a false null hypothesis
A Type II error (β) occurs when you fail to detect a real effect — failing to reject a false null hypothesis.
Question 2: A pharmacist records pill weights: 98, 100, 102, 100, 99, 101, 100. What is the mode?
- 100 (Correct answer)
- 100.0
- 99
- 101
Correct answer: 100
100 appears three times, more than any other value, making it the mode.
Question 3: What does a correlation coefficient of r = -0.85 indicate?
- A strong negative linear relationship (Correct answer)
- A weak negative linear relationship
- A strong positive linear relationship
- No linear relationship
Correct answer: A strong negative linear relationship
Values of r close to -1 indicate a strong negative linear relationship between two variables.
Question 4: In a right-skewed distribution, which ordering is correct?
- Mean > Median > Mode (Correct answer)
- Mode > Median > Mean
- Mean = Median = Mode
- Median > Mean > Mode
Correct answer: Mean > Median > Mode
In a right-skewed distribution, the tail pulls the mean higher than the median, which is higher than the mode.
Question 5: A study finds that taking aspirin reduces headache duration. This is an example of what type of relationship?
- Causal relationship (Correct answer)
- Correlational relationship
- Spurious relationship
- Confounded relationship
Correct answer: Causal relationship
Randomized controlled experiments establish causal relationships when confounders are properly controlled.
Question 6: What is the interquartile range (IQR) of the dataset {3, 5, 7, 9, 11, 13, 15}?
- 8 (Correct answer)
- 6
- 10
- 12
Correct answer: 8
Q1 = 5, Q3 = 13, so IQR = 13 - 5 = 8.
Question 7: Which sampling method ensures every member of a population has an equal chance of being selected?
- Simple random sampling (Correct answer)
- Stratified sampling
- Cluster sampling
- Convenience sampling
Correct answer: Simple random sampling
Simple random sampling gives every individual an equal and independent probability of being selected.
PCAT Statistics 3
Which of the following best describes a Type II error?