AP Statistics Two Categorical Variables and Two-Way Tables Worksheet (PDF)

Name the explanatory and response variable. (a) Researchers ask whether the type of breakfast (cereal, eggs, none) is related to alertness (alert or not) in class. (b) A school asks whether the grade level affects whether students buy lunch.

A survey of 100 students asked whether they own a bike. Of the 40 sophomores, 24 own a bike. Of the 60 juniors, 30 own a bike. Complete a two-way table.

Find the marginal relative frequency of students who read daily, and of students in Grade 10.

Using the table of 200 students, find the percent of all students who are in Grade 11 and do not read daily.

Of the Grade 9 students, what percent read daily? Of the Grade 11 students?

Of the students who read daily, what percent are in each grade?

Make a segmented bar graph of the reading habit within each grade and describe any association.

The graph compares the percent of students passing a class under two phone policies (200 students each). How many in each group passed? Is there an association?

In a study of 500 adults, 60 of the 150 smokers and 40 of the 350 nonsmokers have a cough. Find the percent of smokers who cough and the percent of coughers who smoke.

A school has 400 students. Fifty percent are girls. Of the girls, 30% are in band; of the boys, 20% are in band. Make the two-way table of counts.

Two tutoring programs are compared by pass rates. In the easy course, Program X: 72 of 80 passed; Program Y: 10 of 10 passed. In the hard course, Program X: 2 of 20 passed; Program Y: 12 of 90 passed. Find the pass rate for each program in each course and overall.

Explain why Program X looks better overall in the previous problem even though Program Y has the higher pass rate in each course.

In a sample, 30% of boys and 30% of girls prefer online classes. Are sex and class preference associated? Explain.

A study finds that students who eat breakfast have a higher percent of passing grades. A news story says breakfast improves grades. Is that justified? Explain.

Some owners rated a pet-store ad. Find the percent of cat owners who like the ad and the percent of dog owners who like it. Is there an association?

Write two sentences describing the association in the pet-ad table using conditional percents.

A survey of 250 people shows 140 are female. Of 90 people who prefer tea, 63 are female. Find the number of males who prefer coffee (assuming only tea or coffee).

If sex and drink preference were unrelated, the percent of females preferring tea would equal the overall percent preferring tea (90 of 250). Find the expected number of females who prefer tea among the 140 females, and compare with 63.

A county reports that 1,200 of 4,000 teenagers vape. Among the 1,500 teens from rural areas, 540 vape. Find the percent of rural teens who vape and of non-rural teens who vape.

At a school, 35% of the 600 students ride the bus. Of the bus riders, 40% are in grade 9. How many bus riders are in grade 9, and what percent of all students is that?