Q: How are expected frequencies calculated in a chi-square test of independence for a two-way table?

$$\text{Expected frequency} = \frac{\text{Row total} \times \text{Column total}}{\text{Grand total}}$$

Q: In a chi-square test of independence with a $$3 \times 2$$ table, what is the correct formula for degrees of freedom?

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

Question 1

Which of the following best describes the null hypothesis for a chi-square goodness-of-fit test comparing the age distribution of West Nile Virus (WNV) cases to the general population?

Accepted Answer

The age distribution among WNV cases matches the age distribution in the general population.

Question 2

Given the following observed and expected counts for WNV cases by age group: 0-44 (Observed: 240, Expected: 562.0), 45-64 (Observed: 335, Expected: 144.5), 65-100 (Observed: 198, Expected: 66.5), what is the formula for calculating the chi-square statistic?

Accepted Answer

$$\sum \frac{(O_i - E_i)^2$}{E_i}$$

Question 3

In the WNV age group analysis, the standardized residual for the 0-44 age group is -13.6. What does this indicate?

Accepted Answer

The 0-44 age group is significantly under-represented among WNV cases.

Question 4

How are expected frequencies calculated in a chi-square test of independence for a two-way table?

Accepted Answer

$$	ext{Expected frequency} = \frac{	ext{Row total} 	imes 	ext{Column total}}{	ext{Grand total}}$$

Question 5

Which of the following is a correct interpretation of a chi-square test result with $$\$$chi^2$$ = 693.8$$, $$df = 2$$, and $$p-$$value $$\u003c 0.001$$ when comparing WNV cases by age group to census data?

Accepted Answer

There is a statistically significant difference in the age distribution of WNV cases compared to the general population.

Question 6

What is the correct formula for the degrees of freedom in a chi-square goodness-of-fit test with $$k$$ categories?

Accepted Answer

$$df = k - 1$$

Question 7

A researcher wants to test whether WNV mortality rates differ by age group among diagnosed patients. Which chi-square test should be used?

Accepted Answer

Chi-square test of independence

Question 8

Which of the following is NOT an assumption of the chi-square test?

Accepted Answer

The chi-square statistic can be negative.

Question 9

In a chi-square test of independence with a $$3 	imes 2$$ table, what is the correct formula for degrees of freedom?

Accepted Answer

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

Question 10

A chi-square test yields a large test statistic and a very small $$p-$$value. What does this imply about the null hypothesis?

Accepted Answer

There is strong evidence against the null hypothesis.

Question 11

Which of the following best describes the shape of the chi-square distribution?

Accepted Answer

It is right-skewed, with the degree of skewness decreasing as degrees of freedom increase.

Question 12

In the context of the WNV study, which age group was most over-represented among diagnosed cases compared to the general population?

Accepted Answer

65-100 years

Question 13

If a chi-square test of independence is performed on a $$2 	imes 2$$ table and the $$p-$$value is 0.0009, what is the correct interpretation at $$\alpha = 0.05$$?

Accepted Answer

There is a statistically significant association between the two categorical variables.

Question 14

Which of the following is the correct formula for a standardized residual in a chi-square test?

Accepted Answer

$$\frac{O - E}{\sqrt{E}}$$

Question 15

A study of lion hunting behavior found a chi-square statistic of 10.98 with 1 degree of freedom and a $$p-$$value of 0.0009. What does this result suggest?

Accepted Answer

There is a significant association between position in the line and role in the hunt.

Question 16

Which of the following scenarios would be most appropriate for a chi-square test of homogeneity?

Accepted Answer

Comparing the distribution of blood types across different hospitals.

Question 17

If the expected frequency in a cell of a chi-square test is less than 5, what is the most appropriate action?

Accepted Answer

Combine categories to increase expected frequencies.

Question 18

Which of the following statements about the $$p-$$value in a chi-square test is correct?

Accepted Answer

It represents the probability of observing a chi-square statistic as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true.

Question 19

In a chi-square test, what does a standardized residual greater than 2 or less than -2 typically indicate?

Accepted Answer

The observed frequency in that cell is significantly different from the expected frequency.

Question 20

Which of the following is a real-world example where a chi-square test of independence would be appropriate?

Accepted Answer

Testing whether smoking status is associated with lung cancer diagnosis in a hospital population.

Chi-square Tests: Applications and Interpretation in Epidemiology

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