Two-Way Tables Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
Construct a two-way table from this information: 200 students surveyed; 120 prefer online learning; 80 prefer in-person. Of online learners: 90 passed. Of in-person learners: 55 passed. Complete the table and find whether learning mode and passing are independent.

Solution

  1. 1
    Table: Online-Pass=90, Online-Fail=30, In-Person-Pass=55, In-Person-Fail=25
  2. 2
    P(Pass|Online) = 90/120 = 0.75; P(Pass|In-Person) = 55/80 = 0.6875
  3. 3
    P(Pass) = 145/200 = 0.725
  4. 4
    Independence check: P(Pass|Online)=0.75 ≠ 0.725=P(Pass) → NOT independent; online learners pass at a higher rate

Answer

P(Pass|Online)=0.75 > P(Pass|In-person)=0.6875. Variables are NOT independent.
If P(Pass|Online) = P(Pass) = P(Pass|In-person), the variables are independent. Here, pass rate varies by mode (75% vs 69%), indicating dependence. Whether this is causal or due to confounders (motivated students choose online) requires experimental data.

About Two-Way Tables

A table that displays frequencies for two categorical variables simultaneously, organized with one variable in rows and the other in columns. It shows joint frequencies (individual cells), marginal frequencies (row/column totals), and enables calculation of conditional frequencies.

Learn more about Two-Way Tables →

More Two-Way Tables Examples

Example 1 medium

A two-way table shows: Smoker/Cancer=30, Smoker/No-Cancer=70, Non-smoker/Cancer=20, Non-smoker/No-Ca

Example 2 hard

From a 2×2 table: Group/Outcome frequencies: A-Success=40, A-Fail=10, B-Success=25, B-Fail=25. Test

Example 3 easy

A two-way table: Left-handed/Male=12, Left-handed/Female=8, Right-handed/Male=88, Right-handed/Femal

← All Two-Way Tables Examples Two-Way Tables Concept