Acupuncture and pregnancy A study reported in the medical journal Fertility and Sterility sought to determine whether the ancient Chinese art of acupuncture could help infertile women become pregnant. One hundred sixty healthy women who planned to have IVF were recruited for the study. Half of the subjects 80were randomly assigned to receive acupuncture 25minutes before embryo transfer and again 25minutes after the transfer. The remaining 80women were assigned to a control group and instructed to lie still for 25minutes after the embryo transfer. Results are shown in the table below.


Acupuncture
Control group
Pregnant3421
Not pregnant4659
Total8080

Is the pregnancy rate significantly higher for women who received acupuncture? To find out, researchers perform a test of H0:P1=P2versus Hα;P1>P2, whereP1&P2are the actual pregnancy rates for women like those in the study who do and don't receive acupuncture, 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 0.0152Interpret thisP-value in context.

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

(d) What flaw in the design of the experiment prevents us from drawing a cause-and-effect conclusion? Explain.

Short Answer

Expert verified

(a) Two sample ztest can be use.

(b) The p value of 0.0152indicates that there is a 1.52percent chance that there will be no difference in pregnancy rates between the treatment and control groups.

(c) Pregnancies are more common among women who receive acupuncture than among women who do not.

(d) The women in the control group were aware that they had not had acupuncture since they could see it being done to them. This may have an impact on their behaviour, influencing whether or not they become pregnant. This is when the experiment fails.

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=34

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

total number of women in treatment group=80

In the control group, there were a total of 80women.

P1s 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=3480=0.43

P2=2180=0.26

n1p1=80*0.43=34n1p1>10n11-p1=80*(1-0.34)=46n11-p1>10

n2p2=80*0.26=21n2p2>10n21-p2=80*(1-0.26)=59n21-p2>10

The women's groups are treated as independent because the experiment is randomized. 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 sampleztest can be use.

03

Part (a) Step 1: Given Information 

Given in the question that the p value is0.0152we have to interpret p value of the significance test.

04

Part (b) Step 2: Explanation  

The p value is the probability that the null hypothesis is correct. The p value of 0.0152 indicates that there is a 1.52percent chance that there will be no difference in pregnancy rates between the treatment and control groups.

05

Part (c)  Step 1: Given Information  

Given in the question that the value of p is 0.0152and the significance level isα=0.05. we have to know the conclusion drawn n significance test at 5% level of significance.

06

Part (c) Step 2: Explanation  

The p value of 0.0152is less than the 0.05level of significance. The 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 proportion of pregnancies among women who receive acupuncture is higher than among women who do not.

07

Part (d)  Step 1: Given Information  

We have to find out that at what flaw in the design of the experiment prevents us from drawing a cause-and-effect conclusion.

08

Part (d) Step 2: Explanation  

The women in the control group were aware that they had not had acupuncture since they could see it being done to them. This may have an impact on their behaviour, influencing whether or not they become pregnant. This is when the experiment fails.

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Holly carried out the significance test shown below to answer this question. Unfortunately, she made some mistakes along the way. Identify as many mistakes as you can, and tell how to correct each one.

State: I want to perform a test of

H0:p1=p2

Ha:p1p2

at the 95%confidence level.

Plan: If conditions are met, I’ll do a one-sample ztest for comparing two proportions.

  • Random The data came from a random sample of 385 black, never-married students.
  • Normal One student’s answer to the question should have no relationship to another student’s answer.
  • Independent The counts of successes and failures in the two groups91,58,117, and 119are all at least 10

Do: From the data, p^1=91149=0.61and p^2=117236=0.46.

Test statistic

z=(0.61-0.46)-00.61(0.39)149+0.46(0.54)236=2.91

p=value From Table A, role="math" localid="1650292307192" P(z2.91)1-0.39820.0018.

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