Question 1

Which of the following is the correct formula for the independent samples t-test when the sample sizes are equal?

Accepted Answer

$$ t = \frac{\bar{X}_1 - \bar{X}_2}{s_p \sqrt{\frac{2}{n}}} $$

Question 2

A researcher wants to compare the mean test scores of two different teaching methods using two independent groups. Which statistical test should they use?

Accepted Answer

Independent samples t-test

Question 3

Which of the following best describes the null hypothesis in a one-way ANOVA?

Accepted Answer

All group means are equal

Question 4

Given the following data: Group A (n=10, $$\bar{X}_A=20$$, $$s_A=4$$), Group B (n=10, $$\bar{X}_B=16$$, $$s_B=5). $$Calculate the pooled variance $$s_p^2$ for an independent samples t-test.

Accepted Answer

$$ s_p^2$ = \frac{(n_1$-1)s_1$^2 + (n_2$-1)s_2$^2}{n_1$ + n_2$ - 2} = \frac{(9)(16) + (9)(25)}{18} = \frac{369}{18} = 20.5 $$

Question 5

Which of the following is the correct formula for the F-ratio in a one-way ANOVA?

Accepted Answer

$$ F = \frac{MS_{between}}{MS_{within}} $$

Question 6

A psychologist measures anxiety levels before and after therapy in the same group of patients. Which test is most appropriate?

Accepted Answer

Related samples t-test

Question 7

Which of the following is the formula for the Pearson correlation coefficient $$r$$?

Accepted Answer

$$ r = \frac{\sum (X - \bar{X})(Y - \bar{Y})}{\sqrt{\sum (X - \bar{X})^2$ \sum (Y - \bar{Y})^2$}} $$

Question 8

Which scenario would require the use of a chi-square test for independence?

Accepted Answer

Testing the association between two categorical variables

Question 9

In a two-way ANOVA, what does a significant interaction effect indicate?

Accepted Answer

The effect of one factor depends on the level of the other factor

Question 10

Which of the following best describes the purpose of post-hoc tests in ANOVA?

Accepted Answer

To determine which specific group means are significantly different after finding a significant F-ratio

Question 11

A researcher finds $$r = 0.85$$ between hours studied and exam scores. What does this indicate?

Accepted Answer

A strong positive linear relationship

Question 12

Which formula is used to calculate the regression line for predicting $$Y$$ from $$X$$?

Accepted Answer

$$ Y = a + bX $$

Question 13

If the calculated $$t$$ value in a hypothesis test is greater than the critical $$t$$ value, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis

Question 14

Which of the following is NOT an assumption of the independent samples t-test?

Accepted Answer

The two samples are related

Question 15

A company wants to test if the average satisfaction score differs between three departments. Which test should they use?

Accepted Answer

One-way ANOVA

Question 16

Which formula is used to calculate the degrees of freedom for the independent samples t-test with equal sample sizes?

Accepted Answer

$$ df = n_1$ + n_2$ - 2 $$

Question 17

Which of the following is the correct formula for the sum of squares between groups in a one-way ANOVA?

Accepted Answer

$$ SS_{between} = \sum n_j (\bar{X}_j - \bar{X}_{grand})^2$ $$

Question 18

Which test would be most appropriate for examining whether the distribution of eye color is independent of gender in a sample of students?

Accepted Answer

Chi-square test for independence

Question 19

If a one-way ANOVA yields a significant result, what is the next step?

Accepted Answer

Conduct post-hoc tests to determine which groups differ

Comprehensive Study Notes: Hypothesis Testing, t-Tests, ANOVA, Correlation, Regression, and Chi-Square

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