Solved: Exercises 23 and 24 involve the following setting. Some women would like to have

Chapter 10, Problem 23

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Exercises 23 and 24 involve the following setting. 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 injecting a fertilized egg into the woman's uterus.

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. Women in the treatment group were intentionally prayed for by several people (called intercessors) who did not know them, a process known as intercessory prayer. The praying continued for three 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 \(H_{0}: \ p_{1}=p_{2}\) versus \(H_{a}: \ p_{1}>p_{2}\) where \(p_{1}\) and \(p_{2}\) 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 \(\alpha=0.05\) significance level? Explain.
(d) The women in the study did not know whether they were being prayed for. Explain why this is important.