Prayer and pregnancy Two hundred women who were about to undergo IVF served as subjects in an experiment. Each subject was randomly assigned to cither a treatment group or at 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 VT. The intercessors did not pray for the women in the control group. Here are the results: 44of the 88women in the treatment group got pregnant, compared to 21out of 81in 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=P2versus Hα:P1>P2, where P1&P2are 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=0.05significance level? Explain.

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

Short Answer

Expert verified

(a) Two sample z test can be used

(b)The p value of0.0007indicates that there is a0.07 percent chance that the pregnancy rates of women in the treatment and control groups are identical.

(c) The percentage of pregnancies among women who prayed for are higher than those who did not.

(d) If the women had realized they were being prayed for, it is possible that their behaviour, whether consciously or unconsciously, might have influenced whether or not they became pregnant.

Step by step solution

01

Part (a)  Step 1: Given Information

Given in the question that

The number of women in the treatment group who became pregnant was =44

In the control group, the number of women who became pregnant was lower. localid="1651964264860" =21

=88total number of women in treatment group

In the control group, there were a total of =81women.

P1is the percentage of women in the treatment group who became pregnant.be the proportion of women who became pregnant in the control group P2.

The null and alternative hypothesis are

H0:P1=P2

Hα:P1>P2

We have to name the appropriate test and check that the conditions for carrying out this test are met.

02

Part (a) Step 2: Explanation

To execute a two-sample z test for proportional differences, the following conditions must be met.

1. The sample should be random

2.np>10

3.n1-p>10

4.The observation should be independent.

P1=4488=0.5

P2=2181=0.26

n1p1=88*05=44

n1p1>10

n11-p1=88*1-0.5=44

n11-p1>10

n2p2=81*0.26=21n2p2>10n21-p2=81*1-0.26=60n21-p2>10

The experiment is randomized, and the women's groups are treated as independent. If one woman becomes pregnant, no information about another woman is revealed. As a result, each group's individual observations are likewise deemed independent.

Therefore two sample z test can be used.

03

Part (b)  Step 1: Given Information 

Given in the question that the p value is .0007we have to interpret the p value of the significance test.

04

Part (b) Step 2: Explanation 

The p value represents the probability that the null hypothesis is correct. The p value of0.0007indicates that there is a0.07 percent chance that the pregnancy rates of women in the treatment and control groups are identical.

05

Part (c)  Step 1: Given Information 

Given in the question that the value of p is 0.007and the significance level isα=0.05. we have to know the conclusion drawn n significance test at5%level of significance.

06

Part (c) Step 2: Explanation 

The p value of 0.0007is less than the significance level of 0.05The null hypothesis is rejected at the level of significance of 5percent. The proportion of pregnancies in the treatment group is higher than in the control group, we conclude. As a result, the percentage of pregnancies among women who prayed for are higher than those who did not.

07

Part (d)  Step 1: Given Information 

We have to know the importance of women in the study not knowing if they were being prayed for.

08

Part (d) Step 2: Explanation 

If the women had realized they were being prayed for, it is possible that their behaviour, whether consciously or unconsciously, might have influenced whether or not they became pregnant.

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