6.9 Justifying a Claim Based on a Confidence Interval for a Difference of Population Proportions

Using a Two-Proportion CI to Make Claims

Key question: Does the confidence interval provide convincing evidence of a difference?

Principle: If 0 is NOT in the confidence interval for ${p_1 - p_2}$, we have convincing evidence that ${p_1 \neq p_2}$.

If CI contains only positive values: Evidence that ${p_1 > p_2}$ If CI contains only negative values: Evidence that ${p_1 < p_2}$ If CI contains 0: No convincing evidence of a difference

Example: A 95% CI for ${p_1 - p_2}$ = ${(0.04, 0.18)}$

Since the interval does not contain 0, we have convincing evidence at the ${\alpha = 0.05}$ level that Group 1 has a higher proportion than Group 2.

The entire interval is positive, meaning Group 1's proportion is plausibly 4 to 18 percentage points higher.