AP STATS Confidence Intervals and Significance Tests

One-sample z-test for a population proportion

When we want to know if a population proportion of success is different from some other value

One-sample z-interval for a population proportion

When we want to estimate a population proportion of success of a categorical variable

One-sample t-test for a population mean OR Matched Pairs t-test for μ

When we want to know if a population mean is different from some value or we want to know if there is a mean difference between treatments in a matched pair experimental design

One-sample t-interval for a population mean

When we want to estimate a population mean or population mean difference in a matched pairs experimental design

Two-sample z-test for the difference between population proportions

When we want to know if the proportion of success of two populations are different or we want to compare the proportion of success for two treatments in an experiment

Two-sample z-interval for the difference between population proportions

When we want to estimate the size of the difference between two population proportions

Two-sample t-test for the difference between population means

When we want to know if the means of two populations are different or we want to compare the mean responses to two treatments in an experiment

Two-sample t-interval for the difference between population means

When we want to estimate the size of the difference between two population means or the size of the difference in mean responses to two treatments in an experiment

Chi-Square Test for Goodness-of-Fit

When we want to know if a population distribution of a categorical variable is equal to a reported/hypothesized distribution

Chi-Square Test for Homogeneity

When we want to know if the distribution of a categorical variable is the same for each of several populations or treatments

Chi-Square Test for Independence

When we want to know if there is an association between two categorical variables in a two-way table

t-test for regression slope

When we want to know if there is a linear relationship between two quantitative variables or we want to know if the LSRL is useful in predicting y from x or we want to know if there is a significant correlation between two quantitative variables

t-interval for a regression slope

When we want to estimate a population the slope of the true regression line predicting one quantitative variable from another