ETS Statistical Analysis 2

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?

Accepted Answer

72.25%

Answer

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?

Accepted Answer

±1.960

Answer

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?

Accepted Answer

Median

Answer

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?

Accepted Answer

88.9%

Answer

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?

Accepted Answer

5

Answer

Degrees of freedom for a goodness-of-fit test equals the number of categories minus 1, so 6 − 1 = 5.

(ETS) Educational Testing Service Practice Test

(ETS) Educational Testing Service Practice Test

ETS Statistical Analysis 2