91Ó°ÊÓ

Prayer and pregnancy 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. \({ }^{17}\) 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.

Step by step solution

01

Identify the Appropriate Test

The appropriate test for comparing two proportions is the two-sample z-test for proportions because we are comparing the pregnancy rates between two independent groups (treatment and control).

02

Check Test Conditions

To use the two-sample z-test, we need to check if: (1) We have two independent random samples from large populations, which is valid as stated in the experimental setup. (2) The sampling distribution for the difference in sample proportions is approximately normal. This is supported if both groups meet the conditions: \( n_1 \hat{p}_1 \geq 10, \; n_1 (1-\hat{p}_1) \geq 10, \; n_2 \hat{p}_2 \geq 10, \; n_2 (1-\hat{p}_2) \geq 10 \), where \( n_1 = 88, \; \hat{p}_1 = \frac{44}{88}, \; n_2 = 81, \; \hat{p}_2 = \frac{21}{81} \). Both conditions are satisfied.

03

Interpret the P-value

A \( P \)-value of 0.0007 means that if the null hypothesis \( H_0: p_1 = p_2 \) is true (no difference in pregnancy rates), the probability of observing such a difference in pregnancy rates (or more extreme) by random chance is 0.07%.

04

Draw Conclusion Using α Level

With \( \alpha = 0.05 \), the \( P \)-value of 0.0007 is less than 0.05, meaning we reject the null hypothesis. Researchers conclude that there is a statistically significant difference in pregnancy rates, with the treatment group having a higher rate.

05

The Importance of Blinding

Blinding is important to prevent bias; if participants know they are being prayed for, psychological effects could potentially influence outcomes. The lack of awareness in both groups ensures that any observed effect on pregnancy can be attributed to the intercessory prayer itself, not psychological influence.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Intercessory Prayer

Intercessory prayer is a type of prayer where individuals, known as intercessors, pray on behalf of others. In the context of this experiment, intercessors prayed for the women who were undergoing IVF treatments. These prayers were conducted without the women knowing who was praying for them or even if they were being prayed for at all.
This kind of setup is designed to remove any potential bias or influence that may come from the woman's knowledge of being prayed for. By ensuring the subjects are unaware of the intercessory prayer, the researchers aim to isolate the effect of the prayer from psychological or placebo effects. This helps ensure that any changes in the outcome can be confidently attributed to the intercessory prayer itself.

Pregnancy Rates

Pregnancy rates in this study refer to the proportion of women who became pregnant in each group: those who received intercessory prayer (treatment group) and those who did not (control group). In statistical terms, a comparison of these rates helps determine if there is a significant difference in outcomes between the groups.
The treatment group had 44 out of 88 women becoming pregnant, yielding a pregnancy rate of \( \hat{p}_1 = \frac{44}{88} \approx 0.5 \) or 50%.
The control group had 21 out of 81 women become pregnant, resulting in a rate of \( \hat{p}_2 = \frac{21}{81} \approx 0.259 \) or 25.9%.
The noticeable difference in these rates forms the basis for performing a statistical test to assess if intercessory prayer significantly impacts pregnancy outcomes.

Significance Level

The significance level, often denoted by \( \alpha \), is a threshold used to decide whether to accept or reject the null hypothesis in statistical tests. In this study, researchers set the significance level at 0.05 (or 5%), meaning they are willing to accept a 5% chance of incorrectly rejecting the null hypothesis (Type I error).
When conducting a statistical test like the two-sample z-test for proportions, the computed \( P \)-value is compared to the significance level. Here, the \( P \)-value of 0.0007 was much lower than the 0.05 threshold. This indicates that there is strong evidence against the null hypothesis, supporting the conclusion that intercessory prayer has a significant effect on increasing pregnancy rates.

Random Assignment

Random assignment is a fundamental process in experimental design, ensuring that each participant has an equal chance of being placed in any of the study groups. In this experiment, women were randomly assigned to either the treatment group or the control group.
The purpose of random assignment is to create comparable groups and control for confounding variables, ensuring that any differences in outcomes can be more confidently attributed to the treatment itself, rather than other extraneous factors.
By randomly assigning women to each group, the researchers aimed to eliminate bias and equalize the distribution of other variables (e.g., age, health conditions) across both the treatment and control groups. This strengthens the validity of the causal conclusions drawn from the experiment.