Q: Given the contingency table of purchase category (Camera or Phone) versus household income, what is the null hypothesis for the chi-squared test of independence?

$$H_0$$: \text{Household income and purchase category are independent}$

Q: How do you calculate the expected count for a cell in a contingency table under the null hypothesis of independence?

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

Q: Which statement best describes the alternative hypothesis in a chi-squared test of independence?

$$H_a$$: \text{At least one conditional probability differs from the others}$

Question 1

Which of the following best describes the purpose of a chi-squared test of independence in the context of business statistics?

Accepted Answer

To determine if two categorical variables are associated in a population.

Question 2

Given the contingency table of purchase category (Camera or Phone) versus household income, what is the null hypothesis for the chi-squared test of independence?

Accepted Answer

$$H_0$$: 	ext{Household income and purchase category are independent}$

Question 3

How do you calculate the expected count for a cell in a contingency table under the null hypothesis of independence?

Accepted Answer

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

Question 4

Which formula is used to compute the chi-squared statistic for a contingency table?

Accepted Answer

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

Question 5

A chi-squared test of independence is performed on a $$2 	imes 3$$ contingency table. What are the degrees of freedom for this test?

Accepted Answer

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

Question 6

In the retail example, the observed chi-squared statistic is 33.925 with 4 degrees of freedom. The p-value is 0.0000008. What is the correct conclusion at $$\alpha = 0.05$$?

Accepted Answer

Reject $$H_0$$; there is evidence that purchase category and income are not independent.

Question 7

Which of the following is NOT an assumption or condition for using the chi-squared test of independence?

Accepted Answer

The variables must be quantitative.

Question 8

Which statement best describes the alternative hypothesis in a chi-squared test of independence?

Accepted Answer

$$H_a$$: 	ext{At least one conditional probability differs from the others}$

Question 9

A chi-squared test of goodness of fit is used to test whether the number of employee absences is uniformly distributed across weekdays. If the observed counts are (30, 20, 35, 40, 25) for Monday to Friday, what is the expected count for each day under $$H_0$$?

Accepted Answer

$$30$$

Question 10

How are the degrees of freedom calculated for a chi-squared goodness-of-fit test with $$k$$ categories and no estimated parameters?

Accepted Answer

$$df = k - 1$$

Question 11

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

Accepted Answer

Right-skewed, with only positive values

Question 12

If a chi-squared test of independence is performed and the p-value is greater than $$\alpha$$, what is the correct interpretation?

Accepted Answer

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

Question 13

Which of the following scenarios is most appropriate for a chi-squared test of goodness of fit?

Accepted Answer

Testing if the distribution of car defects is the same across all days of the week.

Question 14

Suppose you have a $$3 	imes 4$$ contingency table. What is the formula for the degrees of freedom for the chi-squared test of independence?

Accepted Answer

$$df = (3-1)(4-1) = 6$$

Question 15

Which of the following is a limitation of the chi-squared test of independence?

Accepted Answer

It does not specify how the proportions differ if the null hypothesis is rejected.

Question 16

If the observed and expected counts in a chi-squared test are very close, what will be the value of the chi-squared statistic?

Accepted Answer

It will be close to zero.

Question 17

Which Excel function can be used to calculate the p-value for a chi-squared statistic?

Accepted Answer

=CHISQ.DIST.RT(statistic, df)

Question 18

A business wants to know if the day of the week affects the likelihood of employees being absent. Which statistical test should they use?

Accepted Answer

Chi-squared test of goodness of fit

Ch. 18 Chi-Squared Tests: Inference for Counts in Business Statistics

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