ETS Statistical Analysis 3 — Questions and Answers
Question 1: A sample of 25 students has a mean test score of 80 and a standard deviation of 10. What is the standard error of the mean?
- 10
- 4
- 2 (Correct answer)
- 0.4
Correct answer: 2
Standard error = standard deviation / √n = 10 / √25 = 10 / 5 = 2.
Question 2: In simple linear regression, the slope coefficient β₁ represents:
- The y-intercept when x = 0
- The predicted value of y when x = 1
- The expected change in y for a one-unit increase in x (Correct answer)
- The correlation between x and y
Correct answer: The expected change in y for a one-unit increase in x
The slope β₁ quantifies the average change in the dependent variable y for each one-unit increase in the independent variable x.
Question 3: An ANOVA test is used primarily to compare:
- Two sample proportions
- Three or more population means (Correct answer)
- The variance of one sample to a known value
- Two population variances
Correct answer: Three or more population means
Analysis of Variance (ANOVA) tests whether there are significant differences among three or more group means simultaneously.
Question 4: If P(A) = 0.4 and P(B) = 0.3, and A and B are independent events, what is P(A ∩ B)?
- 0.70
- 0.10
- 0.58
- 0.12 (Correct answer)
Correct answer: 0.12
For independent events, P(A ∩ B) = P(A) × P(B) = 0.4 × 0.3 = 0.12.
Question 5: A positively skewed distribution has its tail extending to the right. Which relationship between mean, median, and mode is typically true?
- Mean < Median < Mode
- Mode < Median < Mean (Correct answer)
- Mean = Median = Mode
- Median < Mode < Mean
Correct answer: Mode < Median < Mean
In a positively skewed distribution, extreme high values pull the mean rightward, so Mode < Median < Mean.
Question 6: Which sampling method ensures every possible sample of size n has an equal chance of being selected?
- Stratified random sampling
- Cluster sampling
- Simple random sampling (Correct answer)
- Systematic sampling
Correct answer: Simple random sampling
Simple random sampling gives every possible sample of a given size the same probability of selection.
Question 7: The p-value in a hypothesis test represents:
- The probability that the null hypothesis is true
- The probability of obtaining results as extreme as observed, assuming H₀ is true (Correct answer)
- The probability of a Type II error
- The confidence level of the test
Correct answer: The probability of obtaining results as extreme as observed, assuming H₀ is true
The p-value is the probability of observing a test statistic as extreme as (or more extreme than) the one obtained, given that H₀ is true.
ETS Statistical Analysis 3
A sample of 25 students has a mean test score of 80 and a standard deviation of 10.
What is the standard error of the mean?