ETS Statistical Analysis 3

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?

Accepted Answer

2

Answer

Standard error = standard deviation / √n = 10 / √25 = 10 / 5 = 2.

Question 2

In simple linear regression, the slope coefficient β₁ represents:

Accepted Answer

The expected change in y for a one-unit increase in x

Answer

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:

Accepted Answer

Three or more population means

Answer

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)?

Accepted Answer

0.12

Answer

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?

Accepted Answer

Mode < Median < Mean

Answer

In a positively skewed distribution, extreme high values pull the mean rightward, so Mode < Median < Mean.

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