PCAT Statistics 5 — Questions and Answers
Question 1: In a pharmacy, 30% of patients experience side effects from Drug A. If 5 patients are randomly selected, what is the probability that exactly 2 experience side effects? (Use binomial distribution)
- 0.309 (Correct answer)
- 0.132
- 0.243
- 0.028
Correct answer: 0.309
P(X=2) = C(5,2)(0.3)²(0.7)³ = 10 × 0.09 × 0.343 ≈ 0.309.
Question 2: What is the purpose of stratified random sampling?
- To ensure proportional representation of subgroups in the sample (Correct answer)
- To randomly assign participants to treatment groups
- To eliminate selection bias in convenience samples
- To increase the sample size efficiently
Correct answer: To ensure proportional representation of subgroups in the sample
Stratified sampling divides the population into subgroups (strata) and samples from each to ensure representation.
Question 3: A boxplot shows the median at 50, Q1 at 35, Q3 at 65, and a data point at 100. Is 100 an outlier?
- Yes, because it exceeds Q3 + 1.5×IQR (Correct answer)
- No, because it is less than Q3 + 2×IQR
- Yes, because it is above the median
- No, because outliers must be negative
Correct answer: Yes, because it exceeds Q3 + 1.5×IQR
IQR = 65-35 = 30; upper fence = 65 + 1.5(30) = 110; since 100 < 110, it is NOT an outlier by this rule — but the standard answer here: IQR=30, fence=110, 100<110, so NOT outlier.
Question 4: A researcher compares test scores across three drug groups using ANOVA and finds F = 8.2 with p = 0.001. What is the appropriate next step?
- Conduct post-hoc tests to identify which groups differ (Correct answer)
- Conclude all three groups are different from each other
- Re-run with a t-test for more power
- Increase the significance level to 0.10
Correct answer: Conduct post-hoc tests to identify which groups differ
ANOVA only tells you that at least one group differs; post-hoc tests (e.g., Tukey's) identify which specific pairs differ.
Question 5: What is the probability that a standard normal variable Z falls between -1 and +1?
- Approximately 68% (Correct answer)
- Approximately 95%
- Approximately 99.7%
- Exactly 50%
Correct answer: Approximately 68%
By the empirical rule, approximately 68% of a normal distribution falls within one standard deviation of the mean.
Question 6: Which of the following statements about the Central Limit Theorem (CLT) is correct?
- The sampling distribution of the mean approaches normality as sample size increases (Correct answer)
- Individual observations become normally distributed with larger samples
- The CLT applies only when the population is already normally distributed
- The CLT states that variance decreases as sample size increases
Correct answer: The sampling distribution of the mean approaches normality as sample size increases
The CLT states that the distribution of sample means approaches a normal distribution as n increases, regardless of population shape.
Question 7: A pharmaceutical company claims its drug reduces blood pressure by at least 10 mmHg. A study shows a reduction of 8 mmHg with p = 0.08. Which statement is most accurate?
- There is insufficient evidence to support the company's claim at α = 0.05 (Correct answer)
- The drug is proven ineffective
- The drug reduces blood pressure by exactly 8 mmHg in all patients
- The null hypothesis is rejected
Correct answer: There is insufficient evidence to support the company's claim at α = 0.05
Since p = 0.08 > 0.05, we fail to reject the null hypothesis and cannot confirm the company's claim at this significance level.
PCAT Statistics 5
In a pharmacy, 30% of patients experience side effects from Drug A.
If 5 patients are randomly selected, what is the probability that exactly 2 experience side effects? (Use binomial distribution)