Tests of Differences between Proportions (1 of 5)
An experiment is conducted investigating the longterm effects of
early childhood intervention programs (such as head start). In one
(hypothetical) experiment, the highschool drop out rate of the
experimental group (which attended the early childhood program) and
the control group (which did not) were compared. In the experimental
group, 73 of 85 students graduated from high school. In the control
group, only 43 of 82 students graduated. Is this difference
statistically significant?

The first step in hypothesis testing is
to specify the null hypothesis and an
alternative hypothesis. When testing
differences between proportions, the null hypothesis is that the two
population proportions are equal. That is,
the null hypothesis is:
H_{0}: π_{1} = π_{2}.
The alternative hypothesis is: H_{1}: π_{1} ≠ π_{2}.
In this example, the null hypothesis is:
H_{0}: π_{intervention}  π_{no
intervention} =
0.