Question 1

What is evaluated by the chi-square test for goodness of fit?

Accepted Answer

The chi-square test for goodness of fit evaluates whether the observed proportions for a categorical variable match the expected proportions in a population distribution.

Question 2

A chi-square test for goodness of fit is used to examine the distribution of individuals across three categories, and a chi-square test for independence is used to examine the distribution of individuals in a 2×2 matrix of categories.Which test has the larger value for df?

Accepted Answer

The degrees of freedom (df) for a chi-square test for goodness of fit is calculated as the number of categories minus one (k-1). For a chi-square test for independence in a 2x2 matrix, the df is (rows-1)(columns-1), which is 1. Since the goodness of fit test has three categories, its df is 2, which is larger than the df for the test for independence.

Question 3

When the data form a 2x2 matrix, the phi-coefficient is used to measure effect size for the chi-square test for independence.If other factors are held constant, how does sample size influence the values for phi and chi-square?

Accepted Answer

A larger sample size increases the chi-square value because it is sensitive to sample size, but phi, being a measure of association, remains unaffected by sample size.

Question 4

How do you compute df for the chi-square test for goodness of fit?

Accepted Answer

The answer of How do you compute df for the...

Question 5

A researcher is conducting a chi-square test for independence to evaluate the relationship between gender and preference for three different designs for a new automobile.Each individual in a sample of n = 30 males and n = 30 females selects a favorite design from the three choices.If the researcher obtains a chi-square statistic of χ² = 4.81, what is the appropriate statistical decision for the test?

Accepted Answer

The degrees of freedom for the test are (3-1)(2-1) = 2. The critical value for χ² with 2 degrees of freedom at α = .05 is 5.991, and at α = .01 is 9.210. Since 4.81 is less than both critical values, we fail to reject the null hypothesis.

Question 6

Which of the following is a basic assumption for a chi-square hypothesis test?

Accepted Answer

The chi-square test assumes that the observations are independent. It does not require a normal distribution or interval/ratio scale data.

Question 7

Under what circumstances will the chi-square test for goodness of fit produce a large value for chi-square?

Accepted Answer

A large chi-square value indicates that the observed sample proportions are significantly different from the hypothesized population proportions, suggesting a poor fit.

Question 8

A chi-square test for independence has df = 2.What is the total number of categories (cells in the matrix) that were used to classify individuals in the sample?

Accepted Answer

The degrees of freedom (df) for a chi-square test for independence is calculated as (rows - 1) * (columns - 1). If df = 2, possible combinations could be a 2x3 or 3x2 matrix, which results in 6 total categories (cells).

Question 9

Under what circumstances should the chi-square statistic not be used?

Accepted Answer

The chi-square statistic should not be used if the expected frequency (f_e) is less than 5 for any cell, as it may lead to inaccurate results.

Question 10

A sample of 100 people is classified by gender (male/female) and by whether or not they are registered voters.The sample consists of 80 females and 20 males, and has a total of 60 registered voters.If these data were used for a chi-square test for independence, what is the expected frequency for males who are registered voters?

Accepted Answer

The expected frequency for males who are registered voters is calculated by multiplying the total number of males (20) by the proportion of registered voters (60/100), which equals 12.

Question 11

A chi-square test for independence is used to evaluate the relationship between two variables.If both variables are classified into 2 categories, then what is the df value for the chi-square statistic?

Accepted Answer

The degrees of freedom (df) for a chi-square test for independence is calculated as (number of rows - 1) * (number of columns - 1). With both variables having 2 categories, df = (2-1)*(2-1) = 1.

Question 12

In a chi-square test for independence or goodness of fit _____.

Accepted Answer

In a chi-square test for independence or goodness of fit, both Σf_e = n and Σf_e = Σf_o are true. The first equation represents the total number of observations, while the second equation represents the expected frequency based on the null hypothesis (equal frequency for all categories in a goodness of fit test or no association between two variables in a test for independence).

Question 13

Under what conditions is Cramér's V used to measure effect size for a chi-square test for independence?

Accepted Answer

The answer of Under what conditions is Cramér's V used...

Question 14

A sample of 100 people is classified by gender (male/female) and by whether or not they are registered voters.The sample consists of 80 females and 20 males, and has a total of 60 registered voters.If these data are used for a chi-square test for independence, what is the total number of females for the expected frequencies?

Accepted Answer

The total number of females in the sample is 80, which remains constant regardless of the chi-square test calculations. The expected frequencies calculation does not change the total number of individuals in each category; it only redistributes them based on the assumption of independence between variables (gender and voter registration status in this case).

Question 15

A chi-square test for goodness of fit is used to examine the distribution of individuals across four categories, and a chi-square test for independence is used to examine the distribution of individuals across the six categories in a 2×3 matrix of categories.Which test has the larger value for df?

Accepted Answer

The answer of A chi-square test for goodness of fit...

Question 16

What is stated by the null hypothesis for the chi-square test for independence?

Accepted Answer

The null hypothesis for the chi-square test for independence states that there is no relationship between the two variables being analyzed.

Question 17

A chi-square test for independence is being used to evaluate the relationship between two variables, one of which is classified into 3 categories and the second of which is classified into 4 categories.The chi-square statistic for this test would have df equal to ______.

Accepted Answer

The degrees of freedom (df) for a chi-square test for independence is calculated as (number of categories in variable 1 - 1) * (number of categories in variable 2 - 1). Here, (3-1)*(4-1) = 2*3 = 6.

Question 18

A researcher selects a sample of 100 people to investigate the relationship between gender (male/female) and registering to vote.The sample consists of 40 females, of whom 30 are registered voters, and 60 males, of whom 40 are registered voters.If these data were used for a chi-square test for independence, what is the observed frequency for registered males?

Accepted Answer

The observed frequency for registered males is directly given as 40.

Question 19

A chi-square test for independence has df = 3.What is the total number of categories (cells in the matrix) that were used to classify individuals in the sample?

Accepted Answer

The degrees of freedom (df) for a chi-square test for independence is calculated as (rows - 1) * (columns - 1). Given df = 3, the possible combination is 4 categories (2x4 or 4x2), resulting in 8 cells.

Question 20

A researcher selects a sample of 100 people to investigate the relationship between gender (male/female) and registering to vote.The sample consists of 40 females, of whom 30 are registered voters, and 60 males, of whom 40 are registered voters.If these data were used for a chi-square test for independence, what is the expected frequency for registered females?

Accepted Answer

To calculate the expected frequency for registered females, we first need to calculate the overall proportion of registered voters in the sample:
(Number of registered voters / Total sample size) = (30+40) / 100 = 0.7
Then, we can use this proportion to calculate the expected frequency for registered females:
(Expected frequency for registered females) = (Total number of females) x (Proportion of registered voters)
Expected frequency for registered females = 40 x 0.7 = 28. Therefore, the best choice for the expected frequency for registered females is B) 28.

Quiz 17: Chi-Square Tests