Question 1

For a fixed level of significance,the critical value for chi-square increases as the size of the sample increases.​

Accepted Answer

The critical value for chi-square depends on the level of significance and the degrees of freedom, not directly on the sample size. However, degrees of freedom can be related to sample size in specific tests.

Question 2

The chi-square test for goodness of fit evaluates the distribution for one variable,and the test for independence evaluates the relationship between two variables.​

Accepted Answer

This is correct. The chi-square test for goodness of fit is used to determine if an observed distribution fits a theoretical or expected distribution, while the test for independence is used to determine if two variables are related or independent.

Question 3

The chi-square statistic measures how well the data fit the hypothesis,and the symbol is χ².

Accepted Answer

The chi-square statistic is used to assess how well observed data fit a particular hypothesis, and it is represented by the symbol χ².

Question 4

For a fixed level of significance,the critical value for chi-square increases as the degrees of freedom increase.​

Accepted Answer

As the degrees of freedom increase, the chi-square distribution becomes more spread out and the critical value increases. Therefore, for a fixed level of significance, the critical value for chi-square increases as the degrees of freedom increase.

Question 5

A chi-square test for independence produces a chi-square statistic with df = 2.The data for this research study form a matrix with four separate cells.​

Accepted Answer

A chi-square test for independence with df = 2 requires at least a 2 x 2 contingency table, which has four cells. It is possible to have larger contingency tables with more cells, but the minimum requirement is a 2 x 2 table. Therefore, the matrix with four separate cells cannot produce a chi-square statistic with df = 2.

Question 6

For the chi-square test for goodness-of-fit,the researcher must select a sample with an equal number of individuals in each category.​

Accepted Answer

The researcher does not necessarily need to select a sample with an equal number of individuals in each category. However, the expected frequencies of each category should be at least 5 for the chi-square test to be valid.

Question 7

The chi-square test for independence uses the same formula for the chi-square statistic as the chi-square test for goodness-of-fit.​

Accepted Answer

The chi-square test for independence and the chi-square test for goodness-of-fit both use the same formula for the chi-square statistic, which is calculated as the sum of the squared differences between the observed and expected frequencies, divided by the expected frequencies. However, the difference between the two tests lies in their hypotheses and the way the expected frequencies are calculated. The chi-square test for independence is used to determine whether there is a significant association between two categorical variables, while the chi-square test for goodness-of-fit is used to assess whether an observed frequency distribution fits a hypothesized frequency distribution.

Question 8

A large value for the chi-square statistic indicates a large discrepancy between the sample data and the hypothesis.​

Accepted Answer

This is true because the chi-square statistic measures the difference between observed and expected frequencies, and a larger value indicates a greater difference or discrepancy.

Question 9

The observed frequencies for a chi-square test are always whole numbers (no fractions or decimals).​

Accepted Answer

The observed frequencies in a chi-square test can only take on whole number values, as they represent the actual numbers of individuals or events in each category being tested. Fractions or decimals would not make sense in this context.

Question 10

The chi-square test for independence is similar to an independent-measures t test because it can be used to evaluate the difference between two populations or two treatment conditions.​

Accepted Answer

The answer of The chi-square test for independence is similar...

Question 11

For a chi-square test,the expected frequencies are calculated values that are intended to produce a sample that is representative of the null hypothesis.​

Accepted Answer

The statement is true. Expected frequencies are calculated based on the null hypothesis and are used to assess whether the observed frequencies of the sample are significantly different from what would be expected under the null hypothesis.

Question 12

For a chi-square test,the observed frequencies are obtained from the sample.​

Accepted Answer

The observed frequencies are the actual values obtained from the sample, which are used to calculate the chi-square statistic in a chi-square test.

Question 13

Tests that concern parameters and require assumptions about parameters are called parametric tests.​

Accepted Answer

This statement is true. Parametric tests involve making assumptions about the population parameters being tested, such as assuming that the data is normally distributed or that the variances are equal between groups. Examples of parametric tests include t-tests, ANOVA, and linear regression.

Question 14

The data for a chi-square test for independence can be viewed either as representing one sample with two measurements for each participant or as two (or more)separate samples.​

Accepted Answer

In a chi-square test for independence, the data can be viewed as representing one sample with two measurements for each participant or as two (or more) separate samples. This is true. Therefore, option A is correct.

Question 15

One characteristic of nonparametric tests is that they make few,if any,assumptions about the populations being investigated.​

Accepted Answer

Nonparametric tests are not based on any assumption about the parameter of the population. They are used when the distribution of the data is unknown or if the data is not normally distributed. They do not rely on parameters like mean or standard deviation, but rather on ranks or categorical data. Hence, they make few, if any, assumptions about the populations being investigated.

Question 16

​One characteristic of the chi-square tests is that they can be used when the data are measured on a nominal scale.

Accepted Answer

Chi-square tests are commonly used to analyze categorical data, which are often measured on a nominal scale. Therefore, they can be used when the data are measured on a nominal scale.

Question 17

The chi-square distribution tends to be symmetrical with a mean of μ = 0.​

Accepted Answer

The chi-square distribution is not necessarily symmetrical and the mean of the distribution depends on the degrees of freedom parameter. While it is true that for larger degrees of freedom the distribution becomes more symmetrical, it is not always the case that the mean is equal to 0.

Question 18

For both the chi-square test for goodness of fit and the chi-square for independence,Σf_e = n.

Accepted Answer

This is true for both the chi-square tests as they both involve comparing the observed frequencies with the expected frequencies, and the sum of the observed frequencies (f) times the corresponding deviation from the expected frequency (_e) equals the total number of observations (n).

Question 19

In general,a large value for chi-square indicates a good fit between the sample data and the null hypothesis.​

Accepted Answer

A large value for chi-square indicates a poor fit between the sample data and the null hypothesis, meaning that the null hypothesis should be rejected.

Question 20

The chi-square test for independence is similar to a correlation because it evaluates the relationship between two variables.​

Accepted Answer

The chi-square test for independence and correlation are both statistical techniques that examine the relationship between two variables, making the statement true. However, the methods they use to measure this relationship are different. The chi-square test determines whether two categorical variables are independent of each other, while correlation measures the strength and direction of the linear relationship between two continuous variables.

Quiz 17: The Chi-Square Statistic: Tests for Goodness of Fit and Independence

For a fixed level of significance,the critical value for chi-square increases as the size of the sample increases.​

The chi-square test for goodness of fit evaluates the distribution for one variable,and the test for independence evaluates the relationship between two variables.​

The chi-square statistic measures how well the data fit the hypothesis,and the symbol is χ2.​

For a fixed level of significance,the critical value for chi-square increases as the degrees of freedom increase.​

A chi-square test for independence produces a chi-square statistic with df = 2.The data for this research study form a matrix with four separate cells.​

For the chi-square test for goodness-of-fit,the researcher must select a sample with an equal number of individuals in each category.​

The chi-square test for independence uses the same formula for the chi-square statistic as the chi-square test for goodness-of-fit.​

A large value for the chi-square statistic indicates a large discrepancy between the sample data and the hypothesis.​

The observed frequencies for a chi-square test are always whole numbers (no fractions or decimals).​

The chi-square test for independence is similar to an independent-measures t test because it can be used to evaluate the difference between two populations or two treatment conditions.​

For a chi-square test,the expected frequencies are calculated values that are intended to produce a sample that is representative of the null hypothesis.​

For a chi-square test,the observed frequencies are obtained from the sample.​

Tests that concern parameters and require assumptions about parameters are called parametric tests.​

The data for a chi-square test for independence can be viewed either as representing one sample with two measurements for each participant or as two (or more)separate samples.​

One characteristic of nonparametric tests is that they make few,if any,assumptions about the populations being investigated.​

​One characteristic of the chi-square tests is that they can be used when the data are measured on a nominal scale.

The chi-square distribution tends to be symmetrical with a mean of μ = 0.​

For both the chi-square test for goodness of fit and the chi-square for independence,Σfe = n.​

In general,a large value for chi-square indicates a good fit between the sample data and the null hypothesis.​

The chi-square test for independence is similar to a correlation because it evaluates the relationship between two variables.​

For a fixed level of significance,the critical value for chi-square increases as the size of the sample increases.

The chi-square test for goodness of fit evaluates the distribution for one variable,and the test for independence evaluates the relationship between two variables.

The chi-square statistic measures how well the data fit the hypothesis,and the symbol is χ².

For a fixed level of significance,the critical value for chi-square increases as the degrees of freedom increase.

A chi-square test for independence produces a chi-square statistic with df = 2.The data for this research study form a matrix with four separate cells.

For the chi-square test for goodness-of-fit,the researcher must select a sample with an equal number of individuals in each category.

The chi-square test for independence uses the same formula for the chi-square statistic as the chi-square test for goodness-of-fit.

A large value for the chi-square statistic indicates a large discrepancy between the sample data and the hypothesis.

The observed frequencies for a chi-square test are always whole numbers (no fractions or decimals).

The chi-square test for independence is similar to an independent-measures t test because it can be used to evaluate the difference between two populations or two treatment conditions.

For a chi-square test,the expected frequencies are calculated values that are intended to produce a sample that is representative of the null hypothesis.

For a chi-square test,the observed frequencies are obtained from the sample.

Tests that concern parameters and require assumptions about parameters are called parametric tests.

The data for a chi-square test for independence can be viewed either as representing one sample with two measurements for each participant or as two (or more)separate samples.

One characteristic of nonparametric tests is that they make few,if any,assumptions about the populations being investigated.

One characteristic of the chi-square tests is that they can be used when the data are measured on a nominal scale.

The chi-square distribution tends to be symmetrical with a mean of μ = 0.

For both the chi-square test for goodness of fit and the chi-square for independence,Σf_e = n.

In general,a large value for chi-square indicates a good fit between the sample data and the null hypothesis.

The chi-square test for independence is similar to a correlation because it evaluates the relationship between two variables.