Q: In a chi-square test of independence, the expected frequency for a cell is calculated using which formula?

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

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

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

Question 3

Given the observed and expected frequencies for four categories, what are the degrees of freedom for the chi-square goodness-of-fit test?

Accepted Answer

$$k-1$$

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 using which formula?

Accepted Answer

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

Question 7

A chi-square test for independence is performed on a 2x4 contingency table. What are the degrees of freedom for this test?

Accepted Answer

$$(2-1) 	imes (4-1) = 3$$

Question 8

Which of the following statements about the chi-square distribution is correct?

Accepted Answer

It is always a right-tailed test

Question 9

If the calculated chi-square statistic is less than the critical value at $$\alpha = 0.05$$, what is the correct decision?

Accepted Answer

Fail to reject the null hypothesis

Question 10

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

Accepted Answer

The samples must have equal means

Question 11

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

Accepted Answer

The ratio of variance between groups to variance within groups

Question 12

Given three teaching methods with sample sizes of 10 each, what are the degrees of freedom for the numerator and denominator in a one-way ANOVA?

Accepted Answer

Numerator: $$k-1=2$$, Denominator: $$N-k=27$$

Question 13

Which formula is used to calculate the mean square between groups in ANOVA?

Accepted Answer

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

Question 14

A researcher compares three methods for teaching fire safety to children. Which statistical test should be used to determine if there are significant differences among the methods?

Accepted Answer

One-way ANOVA

Question 15

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

Accepted Answer

Reject the null hypothesis

Question 16

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

Accepted Answer

All group means are equal

Question 17

A chi-square test is performed and the calculated value is 2.66 with 3 degrees of freedom. Using the critical values table, what is the correct interpretation at $$\alpha = 0.05$$?

Accepted Answer

Fail to reject the null hypothesis because $$2.66 \u003c 7.815$$

Question 18

Which of the following is the correct formula for the mean square within groups in ANOVA?

Accepted Answer

$$MS_W = \frac{SS_W}{df_D}$$

Question 19

In the context of a chi-square test of independence, what does it mean if the null hypothesis is rejected?

Accepted Answer

There is evidence of an association between the variables

Question 20

Which of the following best describes the purpose of ANOVA?

Accepted Answer

To test for differences among three or more group means

Chapter 10- Chi-Square Tests and One-Way ANOVA: Study Notes

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