AP stat conditions

One-sample z interval (proportion)

Used to estimate a proportion from a random sample, requires random sampling, 10% condition, and success-failure conditions.

10% Condition

The sample size must be less than or equal to 10% of the population if sampling without replacement.

Success-Failure Condition

For a sample size n, both np̂ ≥ 10 and n(1-p̂) ≥ 10 must hold true.

One-sample z test (proportion)

Tests if a proportion is equal to a null proportion, requiring the same conditions as the z interval.

Pooled proportion

A combined estimate of proportion used in two-sample z tests that considers data from both samples.

Two-sample z interval (difference in proportions)

Estimates the difference between two proportions, requires random sampling, independent samples, and success-failure conditions.

Independent Groups

Two or more groups in a study that do not influence each other and are treated separately.

One-sample t interval (mean)

Estimates the mean from a random sample, requires the sample to be random, 10% condition, and either normal distribution or large sample.

Normal/Large Sample Condition

For t tests and intervals, the population should be approximately normal, or the sample size should be at least 30.

Paired t interval/test

Used when measuring two related samples, requires random sampling, 10% condition, and that the differences are normally distributed.

t interval for a slope/t test for slope

Tests the significance of the slope in regression, requires LINE conditions: Linear, Independent, Normal, Equal variance.

Chi-square goodness of fit

Tests if a sample matches a population, requires random sampling, 10% condition, and large counts condition.

Large Counts Condition

In chi-square tests, all expected counts must be greater than or equal to 5.

Chi-square test for independence

Tests for independence between two categorical variables, requires random sampling, 10% condition, and large counts.