This ap statistics chi square quiz asks 10 multiple-choice questions on chi-square tests for homogeneity and independence, and each answer comes with a short explanation.
Ten multiple-choice questions on expected counts, degrees of freedom, choosing between homogeneity and independence, conditions, p-values and conclusions. Pick the best answer for each question, then read the explanation to find any slip.
AP StatisticsCommon Core: AP Statistics Unit 3 (2026-27)
🎯 Chi-Square Tests for Homogeneity and Independence – AP Statistics math quiz
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Question 1
In the table, what is the expected count for the Fall row and Track column if season and sport are independent?Sport chosen by season.
A36
B25
C70
D32
Question 2
How many degrees of freedom does a chi-square test have for a two-way table with 4 rows and 3 columns?
A12
B5
C6
D7
Question 3
Random samples of 200 residents were taken separately from each of three cities, and each resident chose a preferred transit mode. Which test fits?Random samples of 200 residents per city.
AChi-square test for independence
BTwo-sample t test for means
CMatched-pairs t test
DChi-square test for homogeneity
Question 4
A random sample of 300 adults is classified by age group and by preferred phone brand. What is the null hypothesis of the chi-square test of independence?
AAge group and preferred phone brand are associated in the population
BThe mean age is the same for every phone brand
CThe sample proportions of each brand are all equal
DAge group and preferred phone brand are independent in the population
Question 5
Each cell shows observed (expected). What is the contribution of the top-left cell to the chi-square statistic?Observed (expected).
A6
B1.2
C0.2
D1
Question 6
A 2 by 2 table has row totals 10 and 90, column totals 20 and 80, and grand total 100. Which condition for the chi-square test fails?
AThe expected count 2 in one cell is less than 5
BThe observed counts are not all equal
CThe row totals are not equal
DThe degrees of freedom are less than 5
Question 7
The curve shows a chi-square statistic of 7.5 with 3 degrees of freedom, so the shaded area is the p-value. What is the decision at \(\alpha=0.05\)?A chi-square test result.
AReject \(H_{0}\), since \(p\approx 0.058\) is close to 0.05
BReject \(H_{0}\), since 7.5 is greater than \(df=3\)
CFail to reject \(H_{0}\), since \(p\approx 0.058\) is greater than 0.05
DAccept \(H_{0}\), since \(p\approx 0.058\) proves independence
Question 8
A homogeneity test comparing preferred lunch among grades 9, 10 and 11 gives \(p=0.03\). Which conclusion at \(\alpha=0.05\) is correct?
AThere is convincing evidence that lunch preference is not distributed the same way in all three grades
BThere is convincing evidence that lunch preference is distributed the same way in all three grades
CThere is convincing evidence that every grade prefers a different lunch
DThere is convincing evidence that grade level causes lunch preference
Question 9
Every count in a 2 by 2 table is doubled. What happens to the chi-square statistic and the degrees of freedom?
AThe statistic stays the same and df doubles
BThe statistic doubles and df stays 1
CThe statistic and df both double
DThe statistic and df both stay the same
Question 10
A chi-square test on a 2 by 2 table gives a statistic of 6.2. What is the p-value?
A0.0450
B0.1023
C0.0128
D0.9872
🎉 Quiz complete!
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How does this quiz work?
Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.
What should you review before the quiz?
Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.
Remember:
Unit 3 of AP Statistics: chi-square tests for homogeneity and independence use a two-way table of counts.
