AP Statistics Unit 8: Inference for Categorical Data: Chi-Square

A die is rolled 60 times and the observed frequencies for each face are recorded. A chi-square goodness-of-fit test is used to check if the die is fair. What are the degrees of freedom?

In a goodness-of-fit test, the expected frequency for one category is $E=2.5$. Should the chi-square test proceed?

A researcher surveys 150 randomly selected students about their preferred study method (solo, group, or tutoring) and tests whether preference is related to major (STEM vs. non-STEM). Which chi-square test is appropriate?

A researcher conducts a chi-square test of independence with ${\chi }^2=15.3$, $df=4$, $p<0.01$. A student says the test shows that column variable $B$ causes changes in row variable $A$. What is the error?

A chi-square test for independence is conducted on a $3\times 4$ contingency table. What are the degrees of freedom?

A chi-square test of homogeneity compares the distribution of preferred music genre across three age groups (teenagers, adults, seniors). The null hypothesis is:

A chi-square goodness-of-fit test is performed on a spinner with 3 sections claimed to be equally likely. The test statistic is ${\chi }^2=5.4$ with $df=2$. The $p$-value is approximately 0.067. At $\alpha =0.05$, is there evidence the spinner is unfair?

The expected cell count for a cell in a $3\times 3$ contingency table with total $n=200$ is computed as follows: the row total is 80 and the column total is 60. What is the expected count?

A chi-square test of independence produces ${\chi }^2=9.2$ with $df=3$. The critical value at $\alpha =0.05$ is 7.815. What is the correct conclusion?

In a goodness-of-fit test with $k=4$ categories, the expected frequencies are each 25 and the observed frequencies are 20, 30, 22, 28. Compute ${\chi }^2$.

A 3×2 contingency table (3 education levels × 2 voting outcomes) shows the following row totals and column totals:

The expected count for the High school/Voted cell is $E_{11}$. Compute ${\chi }^2$ for this cell if the observed count is 40.

In a chi-square test of independence, which of the following conditions must be met to proceed?

I. The data come from a random sample.
II. Expected cell counts are at least 5.
III. All observed counts are at least 5.