Proportional Data Math Example 4

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

Example 4

hard
Compare two proportions: Group A: 30/120 support policy. Group B: 45/150 support policy. Test if the proportions differ using a z-test for difference in proportions.

Solution

  1. 1
    p^A=30/120=0.25\hat{p}_A = 30/120 = 0.25; p^B=45/150=0.30\hat{p}_B = 45/150 = 0.30
  2. 2
    Pooled proportion: p^=30+45120+150=75270โ‰ˆ0.278\hat{p} = \frac{30+45}{120+150} = \frac{75}{270} \approx 0.278
  3. 3
    Standard error: SE=p^(1โˆ’p^)(1nA+1nB)=0.278ร—0.722ร—(1120+1150)=0.2007ร—0.0150โ‰ˆ0.0548SE = \sqrt{\hat{p}(1-\hat{p})\left(\frac{1}{n_A}+\frac{1}{n_B}\right)} = \sqrt{0.278 \times 0.722 \times \left(\frac{1}{120}+\frac{1}{150}\right)} = \sqrt{0.2007 \times 0.0150} \approx 0.0548
  4. 4
    z-score: z=0.25โˆ’0.300.0548โ‰ˆโˆ’0.91z = \frac{0.25 - 0.30}{0.0548} \approx -0.91; โˆฃzโˆฃ=0.91<1.96|z| = 0.91 < 1.96; fail to reject H0H_0

Answer

zโ‰ˆโˆ’0.91z \approx -0.91; no significant difference in proportions at ฮฑ=0.05\alpha=0.05.
Comparing two proportions requires a pooled standard error. The z-statistic measures how many standard errors apart the two proportions are. A small z-value means the observed difference could easily arise by chance.

About Proportional Data

Proportional data expresses quantities as fractions or percentages of a whole, enabling fair comparison across groups of different sizes.

Learn more about Proportional Data โ†’

More Proportional Data Examples

Example 1 easy

In a survey, 45 out of 180 students prefer online learning. Calculate the sample proportion [formula

Example 2 medium

A poll finds [formula] supporting a candidate from [formula] voters. Calculate the standard error of

Example 3 easy

In a class of 25 students, 15 passed the test. Calculate [formula] and find the number expected to p

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