ETS Statistical Analysis 2 — Questions and Answers
Question 1: A researcher finds a correlation of r = 0.85 between two variables. What percentage of variance in the dependent variable is explained by the independent variable?
- 85%
- 72.25% (Correct answer)
- 92.5%
- 0.85%
Correct answer: 72.25%
The coefficient of determination (r²) equals 0.85² = 0.7225, meaning 72.25% of variance is explained.
Question 2: In a two-tailed hypothesis test with α = 0.05, what is the critical z-value that defines the rejection regions?
- ±1.645
- ±1.960 (Correct answer)
- ±2.326
- ±2.576
Correct answer: ±1.960
For a two-tailed test at α = 0.05, each tail contains 2.5%, corresponding to a z-value of ±1.960.
Question 3: Which measure of central tendency is MOST resistant to extreme outliers?
- Mean
- Weighted mean
- Median (Correct answer)
- Mode
Correct answer: Median
The median is resistant to outliers because it depends only on the middle value(s), not on extreme scores.
Question 4: A dataset has a mean of 50 and a standard deviation of 10. Using Chebyshev's theorem, at least what percentage of data falls within 3 standard deviations of the mean?
- 75%
- 88.9% (Correct answer)
- 95%
- 99.7%
Correct answer: 88.9%
Chebyshev's theorem states at least 1 − 1/k² of data falls within k standard deviations; for k=3, this is 1 − 1/9 ≈ 88.9%.
Question 5: In a chi-square goodness-of-fit test, what are the degrees of freedom when testing whether data fits one of 6 categories?
- 4
- 5 (Correct answer)
- 6
- 7
Correct answer: 5
Degrees of freedom for a goodness-of-fit test equals the number of categories minus 1, so 6 − 1 = 5.
Question 6: A z-score of −2.0 indicates that a data point is:
- 2 standard deviations below the mean (Correct answer)
- 2 standard deviations above the mean
- Negative 2 units from the median
- In the 2nd percentile exactly
Correct answer: 2 standard deviations below the mean
A negative z-score indicates the value is below the mean, and −2.0 means it is exactly 2 standard deviations below.
Question 7: Which type of error occurs when a researcher rejects a true null hypothesis?
- Type II error
- Power error
- Type I error (Correct answer)
- Standard error
Correct answer: Type I error
A Type I error (false positive) occurs when the null hypothesis is true but is incorrectly rejected.
ETS Statistical Analysis 2
A researcher finds a correlation of r = 0.85 between two variables.
What percentage of variance in the dependent variable is explained by the independent variable?