# Chi-Square Test & Goodness of Fit – Statistic

### Chi Square Test & Goodness of Fit – Statistc

The key terms in these Statistics chapters include Chi-Square Test, Population, Distribution, Goodness of Fit & The Null Hypothesis.

What values are specified by the null hypothesis for the chi-square test for goodness of fit?

Proportions for the entire population

What happens to the critical value for a chi-square test if the size of the sample is increased?

The critical value depends on the number of categories, not the sample size

What happens to the shape of the chi-square distribution as the df value increases?

The mode (highest point) of the distribution moves to the right

What conclusion is appropriate if a chi-square test produces a chi-square statistic near zero?

There a good fit between the sample data and the null hypothesis

The chi-square test for goodness of fit evaluates

the shape or proportions for a population distribution

A large value for the chi-square statistic indicates

the sample data (observed values) do not fit the null hypothesis

The term expected frequencies refers to

the frequencies computed from the null hypothesis

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

##### Goodness of fit

What values are specified by the null hypothesis for the chi-square test for goodness of fit?

Proportions for the entire population

What happens to the critical value for a chi-square test if the size of the sample is increased?

The critical value depends on the number of categories, not the sample size

What happens to the shape of the chi-square distribution as the df value increases?

The mode (highest point) of the distribution moves to the right

What conclusion is appropriate if a chi-square test produces a chi-square statistic near zero?

There a good fit between the sample data and the null hypothesis

The chi-square test for goodness of fit evaluates

the shape or proportions for a population distribution

The term observed frequency refers to

the frequencies found in the sample data

What is indicated by a large value for the chi-square statistic?

The sample data (observed values) do not match the null hypothesis

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

When the sample proportions are much different than the hypothesized population proportions

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 2X3 matrix of categories. Which test has the larger value for df?

##### Both tests have the same df value

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 six categories in a 2X3 matrix of categories. Which test has the larger value for df?

The test for goodness of fit

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 ere used for a chi-square test for independence, what is the observed frequency for registered males?

40

Nonparametric tests are used only with data from a nominal scale.

False

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.

True

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

##### False

A chi-square test for independence produces a chi-square statistic with df = 2. The data for this research study form a 2X2 matrix with four separate categories.

False

Chi-square values are always greater than or equal to zero.

True

The observed frequencies for a chi-square test can be fractions or decimal values.

False

For a linear regression equation, the standard error of estimate is computed using df =

n – 2

A researcher classifies college students as either high or low IQ, then measures each student’s grade point average. For the resulting data, which correlation should be used to measure the relationship between IQ and grade point average?

point-biserial correlation

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

Chi-Square Test & Goodness of Fit

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

Goodness of fit

A large value for the chi-square statistic indicates

the sample data (observed values) do not fit the null hypothesis

The term expected frequencies refers to

the frequencies computed from the null hypothesis

Nonparametric tests are used only with data from a nominal scale.

False

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.

True

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

False

Chi-square values are always greater than or equal to zero.

True

The observed frequencies for a chi-square test can be fractions or decimal values.

False

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

##### False

A chi-square test for independence produces a chi-square statistic with df = 2. The data for this research study form a 2X2 matrix with four separate categories.

False

What values are specified by the null hypothesis for the chi-square test for goodness of fit?

Proportions for the entire population

What happens to the critical value for a chi-square test if the size of the sample is increased?

The critical value depends on the number of categories, not the sample size

What happens to the shape of the chi-square distribution as the df value increases?

The mode (highest point) of the distribution moves to the right

What conclusion is appropriate if a chi-square test produces a chi-square statistic near zero?

There a good fit between the sample data and the null hypothesis

The chi-square test for goodness of fit evaluates

the shape or proportions for a population distribution

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.

True

For the expected frequencies in a chi-square test for independence, the proportions for any row are exactly the same as the proportions in every other row.

True

A chi-square test should not be used if any observed frequency is less than five.

True

The observed frequencies for a chi-square test can be fractions or decimal values.

False

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

##### False

A chi-square test for independence produces a chi-square statistic with df = 2. The data for this research study form a 2X2 matrix with four separate categories.

False

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

##### False

What conclusion is appropriate if a chi-square test produces a chi-square statistic near zero?

There a good fit between the sample data and the null hypothesis

What happens to the critical value for a chi-square test if the size of the sample is increased?

The critical value depends on the number of categories, not the sample size

A large value for the chi-square statistic indicates

the sample data (observed values) do not fit the null hypothesis

The term expected frequencies refers to

the frequencies computed from the null hypothesis

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

False

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

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