Q: Which of the following is the correct formula for the expected frequency in a cell of a two-way table when performing a chi-square test of independence?

$E_{ij} = \frac{(\text{Row Total}) \times (\text{Column Total})}{\text{Grand Total}}$

Question 1

Which of the following is the correct formula for the expected frequency in a cell of a two-way table when performing a chi-square test of independence?

Accepted Answer

$E_{ij} = \frac{(	ext{Row Total}) 	imes (	ext{Column Total})}{	ext{Grand Total}}$

Question 2

A researcher wants to test whether a six-sided die is fair. She rolls the die 60 times and records the frequency of each outcome. Which statistical test should she use?

Accepted Answer

Chi-square goodness-of-fit test

Question 3

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

Accepted Answer

The data are paired

Question 4

Suppose you toss a fair coin 100 times. What is the expected frequency of heads?

Accepted Answer

$50$

Question 5

The chi-square statistic is calculated as:

Accepted Answer

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

Question 6

A polling organization asks a random sample of people for their political preference (Liberal, Conservative, NDP, Green) and their opinion on minimum wage. Which test should be used to determine if political preference and opinion on minimum wage are related?

Accepted Answer

Chi-square test of independence

Question 7

Which of the following best describes the null hypothesis for a chi-square test of homogeneity?

Accepted Answer

The distributions of the categorical variable are the same across populations

Question 8

If a chi-square test is performed with 4 categories, what are the degrees of freedom for the test?

Accepted Answer

$3$

Question 9

Which of the following conditions must be met for the chi-square approximation to be valid?

Accepted Answer

All expected cell frequencies are at least 5

Question 10

A study is conducted to determine if there is an association between gender (male, female) and preference for three brands of soda (A, B, C). Which test should be used?

Accepted Answer

Chi-square test of independence

Question 11

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

Accepted Answer

It is right-skewed and becomes more symmetric as degrees of freedom increase

Question 12

A random sample of 250 students is classified by year (first, second, third, fourth). The expected frequency for first-year students is 28%. What is the expected count for first-year students?

Accepted Answer

$70$

Question 13

Which of the following is a key difference between the chi-square test of independence and the chi-square test of homogeneity?

Accepted Answer

Test of independence uses one sample, test of homogeneity uses two or more samples

Question 14

Which of the following is the correct formula for the degrees of freedom in a chi-square test for a two-way table with $r$ rows and $c$ columns?

Accepted Answer

$(r-1) 	imes (c-1)$

Question 15

A chi-square test yields a p-value of 0.03. At a significance level of $\alpha = 0.05$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis

Question 16

Which of the following scenarios would require a chi-square goodness-of-fit test?

Accepted Answer

Testing if the distribution of colors in a bag of candies matches the company's claimed distribution

Question 17

If the observed and expected frequencies in a chi-square test are very close, what will happen to the value of the chi-square statistic?

Accepted Answer

It will be small

Question 18

Which of the following is NOT a condition for using the chi-square test?

Accepted Answer

Data are measured on an interval scale

Question 19

A study collects data on marital status (single, married, divorced) and employment status (employed, unemployed) for a random sample of adults. Which test should be used to determine if marital status and employment status are related?

Accepted Answer

Chi-square test of independence

Question 20

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

Accepted Answer

The two categorical variables are related

Chapter 10

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