AP Statistics · Topic 8.4
Expected Counts in Two-Way Tables Practice
Part of Inference for Categorical Data: Chi-Square.(VAR-8.C)
Practice questions
5
Sample questions
5 of 5 — sign in to practice the rest with adaptive difficulty and mastery tracking.
Sample 1difficulty 3/5
Three populations are sampled (n1=80, n2=80, n3=80). Column totals (favor/oppose) are 120 and 120.
What is the expected count for each cell?
- A
60
- Bcheck_circle
40
- C
80
- D
30
Why
Expected = (row × col)/total = (80 × 120)/240 = 40 for every cell.
- A
Sample 2difficulty 3/5
A two-way table records 200 individuals classified by exercise level and reported stress.
What is the expected count for Active and Low Stress?
- A
60
- Bcheck_circle
45
- C
50
- D
55
Why
Expected = (row total × column total)/grand total = (100 × 90)/200 = 45.
- A
Sample 3difficulty 4/5
From the table (n = 100), expected count of "A and Yes" =
- Acheck_circle
35
- B
50
- C
20
- D
25
Why
Row total A = 50; col total Yes = 70; E = 50·70/100 = 35.
- A
Sample 4difficulty 4/5
Expected count for a cell in a chi-square test of independence is
- A
Cell count itself
- Bcheck_circle
(row total × column total)/n
- C
row total + column total
- D
n × proportion
Why
Under independence, E_ij = (r_i × c_j)/n.
- A
Sample 5difficulty 4/5
A 2×2 table: row totals 60, 40; column totals 30, 70; n=100. Expected count for cell (1,1) =
- A
60
- B
12
- C
30
- Dcheck_circle
18
Why
E = 60·30/100 = 18.
- A