Q: Which formula is used to calculate the expected frequency ($$E) in a $$contingency table for a chi-square test?

$$E = \frac{\text{row total} \cdot \text{col total}}{\text{Grand Total}}$$

Question 1

Which of the following best describes the purpose of a Homogeneity Test in statistics?

Accepted Answer

To determine if two or more populations have the same proportion of a certain characteristic.

Question 2

In a Homogeneity Test, what is the null hypothesis ($$H_0$$)?

Accepted Answer

$$H_0$$: All proportions of the characteristic are the SAME for all populations.

Question 3

Which formula is used to calculate the expected frequency ($$E) in a $$contingency table for a chi-square test?

Accepted Answer

$$E = \frac{	ext{row total} \cdot 	ext{col total}}{	ext{Grand Total}}$$

Question 4

A pharmaceutical company tests a new ADHD medication. At the 0.05 significance level, they want to know if symptom improvement is distributed differently between placebo and non-placebo groups. Which test should they use?

Accepted Answer

Chi-square test for homogeneity

Question 5

Given the following observed and expected frequencies for two groups: $$O_1 = 18$, E_1$ = 26.4$$, $$O_2 = 37$, E_2$ = 28.6$$, $$O_3 = 30$, E_3$ = 21.6$$, $$O_4 = 15$, E_4$ = 23.4$$, what is the chi-square statistic ($$\$$chi^2$$)?

Accepted Answer

$$\$$chi^2$$ = \frac{(18-26.4)^2$}{26.4} + \frac{(37-28.6)^2$}{28.6} + \frac{(30-21.6)^2$}{21.6} + \frac{(15-23.4)^2$}{23.4} = 11.42$$

Question 6

What is the correct formula for degrees of freedom ($$df) in a $$chi-square test for a contingency table with $$r$$ rows and $$c$$ columns?

Accepted Answer

$$df = (r-1)(c-1)$$

Question 7

If the p-value for a chi-square test is less than the significance level ($$\alpha$$), what is the correct conclusion?

Accepted Answer

Reject $$H_0$$; there is enough evidence to support a difference.

Question 8

Which of the following is NOT a requirement for using the chi-square test for homogeneity or independence?

Accepted Answer

Each expected frequency ($$E) $$must be less than 5.

Question 9

A researcher wants to test if height and grade level are independent using a chi-square test. Which null hypothesis should they use?

Accepted Answer

$$H_0$$: Height and grade level are independent.

Question 10

In a chi-square test for independence, what does it mean if you fail to reject the null hypothesis?

Accepted Answer

There is not enough evidence to conclude the variables are dependent.

Question 11

Which scenario best fits a chi-square test for independence?

Accepted Answer

Testing if age group affects car ownership.

Question 12

A chi-square test for independence is performed with $$r = 2$$ rows and $$c = 3$$ columns. What is the degrees of freedom?

Accepted Answer

$$df = (2-1)(3-1) = 2$$

Question 13

Which of the following statements is TRUE about the chi-square test for homogeneity?

Accepted Answer

It compares proportions of a characteristic across different populations.

Question 14

If a chi-square test yields a p-value of $$0.0007$$ and the significance level is $$0.05$$, what should you conclude?

Accepted Answer

Reject $$H_0$$; there is enough evidence of a difference.

Question 15

Which formula is used to calculate the chi-square statistic ($$\$$chi^2$$) in a contingency table?

Accepted Answer

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

Question 16

A chi-square test for independence is performed and the p-value is $$0.19$$ with $$\alpha = 0.05. $$What is the correct conclusion?

Accepted Answer

Fail to reject $$H_0$$; there is not enough evidence that the variables are dependent.

Question 17

Which of the following is a requirement for using the chi-square test?

Accepted Answer

Expected frequency for each cell must be at least 5.

Question 18

In a chi-square test for independence, what does the alternative hypothesis ($$H_a) $$state?

Accepted Answer

The variables are dependent.

Question 19

A hospital tests whether the group a participant was in is independent from their symptom improvement. Which test is appropriate?

Accepted Answer

Chi-square test for independence

Chi-Square Tests: Homogeneity, Independence, and Goodness-of-Fit

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