1. Testing p1 – p2 (Case I) Example: The effectiveness of Aspirin
A research project employing 22,000 American physicians was conduct to discover whether aspirin can prevent heart attacks.
Half of the participants in the research took aspirin, and half took placebo.
In a three years period,104 of those who took aspirin and 189 of those who took the placebo had had heart attacks.
Is aspirin effective in preventing heart attacks?

2. The effectiveness of Aspirin
Solution
The problem objective is to compare the population of sales of the two packaging designs.
The data is qualitative (yes/no for the purchase of the new design per customer)
The hypotheses test are H0: p1 - p2 = 0 H1: p1 - p2 > 0
We identify here case 1.
Population 1 – purchases of Design A
Population 2 – purchases of Design B

3. Solving by hand
For a 5% significance level the rejection region is z > za = -z.05 =
< , so reject
the null hypothesis.