Two hundred women who were about to undergo IVF served as subjects in an experiment. Each subject was randomly assigned to either a treatment group or a control group. Several people (called intercessors) prayed intentionally for the women in the treatment group, although they did not know the women, a process known as intercessory prayer. Prayers continued for 3 weeks following IVF. The intercessors did not pray for the women in the control group. Here are the results: 44 of the 88 women in the treatment group got pregnant, compared to 21 out of 81 in the control group.

Is the pregnancy rate significantly higher for women who received intercessory prayer? To find out, researchers perform a test of H₀: p₁ = p₂ versus H_a: p₁ > p₂, where p₁ and p₂ are the actual pregnancy rates for women like those in the study who do and don’t receive intercessory prayer, respectively.

a. Name the appropriate test and check that the conditions for carrying out this test are met.

b. The appropriate test from part (a) yields a P-value of 0.0007. Interpret this P-value in context.

c. What conclusion should researchers draw at the α = 0.05 significance level?

d. The women in the study did not know whether they were being prayed for. Explain why this is important.

Some women would like to have children but cannot do so for medical reasons. One option for these women is a procedure called in vitro fertilization (IVF), which involves fertilizing an egg outside the woman’s body and implanting it in her uterus.