Q: In a chi-square test of independence, the expected frequency for a cell is calculated as:

$$E = \frac{(\text{row total}) \times (\text{column total})}{\text{grand total}}$$

Question 1

A university survey aimed for equal representation from all four undergraduate years. Out of 200 responses, the observed frequencies were: 60 first-year, 45 second-year, 52 third-year, and 43 fourth-year students. What are the expected frequencies for each year if the goal is equal representation?

Accepted Answer

50 for each year

Question 2

Which formula is used to calculate the chi-square test statistic for the goodness-of-fit test?

Accepted Answer

$$\$$chi^2$$ = \sum \frac{(O - E)^2$}{E}$$

Question 3

In a chi-square goodness-of-fit test with 4 categories and 200 observations, what are the degrees of freedom?

Accepted Answer

$$df = 3$$

Question 4

A researcher wants to test if the distribution of grades in a class (A, B, C, D, F) matches the university's policy: 5% A, 20% B, 50% C, 20% D, 5% F. Which statistical test should be used?

Accepted Answer

Chi-square goodness-of-fit test

Question 5

Which of the following is a necessary condition for performing a chi-square goodness-of-fit test?

Accepted Answer

Each expected frequency must be at least 5

Question 6

In a chi-square test of independence, the expected frequency for a cell is calculated as:

Accepted Answer

$$E = \frac{(	ext{row total}) 	imes (	ext{column total})}{	ext{grand total}}$$

Question 7

A chi-square test statistic is calculated as $$\$$chi^2$$ = 7.12$$ with $$df = 3. $$Using the critical values table, what is the correct conclusion at $$\alpha = 0.05$$?

Accepted Answer

Fail to reject $$H_0$$ because $$7.12 \u003c 7.815$$

Question 8

Which of the following best describes the null hypothesis in a chi-square test of independence?

Accepted Answer

The two categorical variables are independent

Question 9

In a one-way ANOVA, what does the F statistic represent?

Accepted Answer

The ratio of variance between groups to variance within groups

Question 10

Which formula correctly calculates the mean square between groups in a one-way ANOVA?

Accepted Answer

$$MS_B = \frac{SS_B}{df_N}$$

Question 11

A researcher compares three teaching methods using a one-way ANOVA. The sum of squares between groups is 120, and the degrees of freedom between groups is 2. What is the mean square between groups?

Accepted Answer

$$MS_B = 60$$

Question 12

Which of the following is NOT an assumption of one-way ANOVA?

Accepted Answer

The samples must have equal means

Question 13

If the calculated F statistic in a one-way ANOVA is greater than the critical value, what is the correct decision?

Accepted Answer

Reject the null hypothesis

Question 14

In the context of ANOVA, what does the term 'factor' refer to?

Accepted Answer

The independent variable being studied

Question 15

A researcher wants to know if test anxiety is related to year of study. Which test should be used?

Accepted Answer

Chi-square test of independence

Question 16

Given the following observed and expected frequencies for a category: O = 30, E = 25. What is the contribution of this category to the chi-square statistic?

Accepted Answer

$$\frac{(30-25)^2$}{25} = 1$$

Question 17

Which of the following best describes the purpose of a one-way ANOVA?

Accepted Answer

To test for differences among three or more group means

Question 18

If the null hypothesis is true in a chi-square goodness-of-fit test, what is the expected value of the chi-square statistic?

Accepted Answer

$$df$$

Question 19

A one-way ANOVA is performed with 4 groups and a total of 40 observations. What are the degrees of freedom for the denominator?

Accepted Answer

$$N - k = 40 - 4 = 36$$

Chi-Square Tests and One-Way ANOVA: Concepts, Calculations, and Applications

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