AP Stats Chapter 11 Flashcards

Questions and Answers

What is the chi-square statistic?

A measure of how far the observed counts are from the expected counts, allowing us to determine whether a hypothesized distribution seems valid.

What is the chi-square formula?

x^2 = sum((observed - expected)^2 / expected)

What does the sampling distribution of the chi-square statistic look like?

Not normal - right-skewed with only positive values.

Can chi-square statistics be negative?

False Signup and view all the answers

What is a chi-square goodness of fit test?

A significance test applied to one categorical variable from a single population to see if sample data are consistent with a hypothesized distribution. Signup and view all the answers

What is df for a chi-square goodness of fit test?

df = number of categories - 1 Signup and view all the answers

What are the conditions for a chi-square goodness of fit test?

Random sample, large sample size (all expected counts at least 5), independent observations. Signup and view all the answers

What do hypotheses look like for a chi-square goodness of fit test?

Ho: The specified distribution of the categorical variable is correct; Ha: The specified distribution of the categorical variable is not correct. Signup and view all the answers

Does the chi-square test statistic compare counts or proportions?

Counts. Signup and view all the answers

What is the chi-square test for homogeneity?

A test used to determine if the distribution of a variable is the same across two or more populations. Signup and view all the answers

What are the hypotheses for a chi-square test for homogeneity?

Ho: There is no difference in the distribution of a categorical variable for several populations; Ha: There is a difference. Signup and view all the answers

What is the degrees of freedom for a chi-square test for homogeneity?

df = (# of rows - 1)(# of columns - 1) Signup and view all the answers

How do you find the expected counts for a two-way table?

Expected count = (row total x column total) / table total. Signup and view all the answers

What are the conditions that must be met to perform a chi-square test for homogeneity?

RANDOM, LARGE SAMPLE SIZE, INDEPENDENT. Signup and view all the answers

When is a chi-square test for association/independence applied?

When testing two categorical variables from one population. Signup and view all the answers

What are the hypotheses for a chi-square test for association/independence?

Ho: There is no association between two categorical variables; Ha: There is an association. Signup and view all the answers

What kind of table do the test for homogeneity and association/independence come from?

A two-way table. Signup and view all the answers

What is the difference between a chi-square test for homogeneity and for association/independence?

Homogeneity comes from several populations, whereas association/independence comes from one population. Signup and view all the answers

Study Notes

Chi-Square Statistic

Measures the difference between observed and expected counts.
Helps validate the hypothesized distribution.

Chi-Square Formula

Formula: x² = Σ((observed - expected)² / expected).

Sampling Distribution of Chi-Square Statistic

Not normally distributed; right-skewed with only positive values.

Chi-Square Statistics and Negativity

Cannot be negative due to the squaring in its calculation.

Chi-Square Goodness of Fit Test

Significance test for one categorical variable from a single population.
Assesses consistency of sample data with a hypothesized distribution.

Degrees of Freedom (df) for Goodness of Fit Test

Calculated as: df = number of categories - 1.

Conditions for Chi-Square Goodness of Fit Test

RANDOM: Data must come from a random sample or experiment.
LARGE SAMPLE SIZE: All expected counts should be at least 5.
INDEPENDENT: Individual observations must be independent; when sampling without replacement, the population should be at least 10 times larger than the sample.

Hypotheses for Chi-Square Goodness of Fit Test

Null Hypothesis (Ho): Specified distribution of the categorical variable is correct.
Alternative Hypothesis (Ha): Specified distribution is not correct.

Chi-Square Test Statistic Comparison

Compares counts, not proportions.

Chi-Square Test for Homogeneity

Used to test if distributions differ across two or more populations.

Hypotheses for Chi-Square Test for Homogeneity

Null Hypothesis (Ho): No difference in distribution across populations.
Alternative Hypothesis (Ha): Difference exists in distribution across populations.

Degrees of Freedom for Chi-Square Test for Homogeneity

Calculated as: df = (number of rows - 1)(number of columns - 1).

Finding Expected Counts in a Two-Way Table

Formula: expected count = (row total x column total) / table total.

Conditions for Chi-Square Test for Homogeneity

Same conditions as the goodness of fit test: RANDOM, LARGE SAMPLE SIZE, INDEPENDENT.

Application of Chi-Square Test for Association/Independence

Used when examining the relationship between two categorical variables from one population.

Hypotheses for Chi-Square Test for Association/Independence

Null Hypothesis (Ho): No association between the two categorical variables.
Alternative Hypothesis (Ha): An association exists between the two categorical variables.

Types of Tables for Homogeneity and Association Tests

Both tests utilize a two-way table for analysis.

Differences Between Tests for Homogeneity and Association/Independence

Homogeneity tests involve several populations, while association/independence tests focus on one population.

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Test your knowledge on key concepts from AP Statistics Chapter 11 with these flashcards. Each card highlights important terms and definitions related to chi-square statistics, including formulas and distributions. Enhance your understanding of statistical analysis in this engaging format.