AP Stats AP Stats Inference for Categorical Data

Question 1

Which chi-square test is used to determine whether the distribution of a categorical variable matches a claimed distribution?

Accepted Answer

Chi-square goodness-of-fit test

Answer

The chi-square goodness-of-fit test compares an observed distribution to an expected (claimed) distribution for a single categorical variable.

Question 2

In a chi-square test, the expected count for each cell is calculated as:

Accepted Answer

(row total × column total) / grand total

Answer

Expected cell count = (row total × column total) / grand total, ensuring marginal totals are preserved under the null hypothesis.

Question 3

What is the minimum expected cell count required in each cell before performing a chi-square test?

Accepted Answer

5

Answer

AP Statistics requires all expected cell counts to be at least 5 for the chi-square approximation to be valid.

Question 4

A chi-square test for independence tests whether two categorical variables are independent. A very small p-value indicates:

Accepted Answer

There is strong evidence against independence

Answer

A small p-value provides strong evidence against the null hypothesis of independence, suggesting the two variables are associated.

Question 5

For a 3×4 contingency table, what are the degrees of freedom for the chi-square test for independence?

Accepted Answer

6

Answer

Degrees of freedom = (rows − 1)(columns − 1) = (3 − 1)(4 − 1) = 2 × 3 = 6.

AP Practice Test