AP Stats Chapter 11 Flashcards

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.