Compare Two Sample Proportions

Compare Two Sample Proportions

When comparing two sample proportions, the key idea is to compare the proportion of successes in each sample.

1) Find each sample proportion

For each group, compute [ \hat p = \frac{\text{number of successes}}{\text{sample size}}. ] Do this separately for both samples.

2) Compare the two proportions

If the task asks for a difference, subtract one from the other: [ \hat p_1 - \hat p_2. ] Pay attention to the order, since reversing it changes the sign.

If the task asks for a ratio or another comparison, use the quantities requested, but still start by finding each sample proportion accurately.

3) Simplify the final answer

Reduce fractions if possible, and write decimals only if the instructions or answer format require it. Keep the result in its simplest form.

4) Check your work

Make sure:

• each proportion is between 0 and 1,
• the counts of successes do not exceed the sample sizes,
• your arithmetic is consistent with the order of comparison.

A good final check is to see whether the result makes sense: if one group has a larger success rate, the difference should reflect that.