Chapter 10.1, Problem 27E

(a)

To determine

To name the appropriate test and check that the conditions for carrying out this test are met.

Answer to Problem 27E

The two sample z test is the appropriate test.

Explanation of Solution

Given:

It is given that two hundred women are about to undergo an IVF served as an subject for experiment and they were chosen randomly to either a treatment group or a control group. And it is also given the hypothesis that:

  $\begin{array}{l}{H}_0:p_1=p_2\\ H_a:p_1>p_2\end{array}$

Therefore, according to the study we want to execute a test about comparing two populations mean this can be done by using the two sample z test for the difference in two proportions.

Conditions to be satisfied:

There are three conditions to be satisfied:

Random: It is satisfied because the women are selected randomly to a treatment group and the control group.

Independent: It can be assumed because the women were randomly assigned to a group.

Normal: It is satisfied because there are $44$ successes and $88-44=44$ failures in the first sample and there are $21$ successes and $81-21=60$ failures in the second sample, which are all at least ten.

Thus, all the conditions are satisfied.

(b)

To determine

To interpret the P -value for this context.

Answer to Problem 27E

The probability of obtaining a difference between the proportions as in this sample or more extreme is $0.07\%$ , if the population proportions are equal.

Explanation of Solution

It is given that the appropriate test given in part (a) yields P value as $0.0007$ . Thus, we have,

  $\begin{array}{l}{H}_0:p_1=p_2\\ H_a:p_1>p_2\\ P=0.0007=0.07\%\end{array}$

Now, the P value is the probability of obtaining the value of the test statistics or a value more extreme if the null hypothesis is true.

Thus, we interpret from the P value that it is the probability of obtaining a difference between the proportions as in this sample or more extreme is $0.07\%$ , if the population proportions are equal.

(c)

To determine

To find out what conclusion the researcher draw at the $\alpha =0.05$ significance level.

Answer to Problem 27E

There is sufficient evidence that the pregnancy rate is higher for women who received intercessory prayer.

Explanation of Solution

It is given that the appropriate test given in part (a) yields P value as $0.0007$ . Thus, we have,

  $\begin{array}{l}{H}_0:p_1=p_2\\ H_a:p_1>p_2\\ P=0.0007=0.07\%\end{array}$

And as we know that if the P value is smaller than the significance level then we reject the null hypothesis. Thus, we have,

  $P<0.05\Rightarrow \text{Reject }{H}_0$

Thus, we conclude that there is sufficient evidence that the pregnancy rate is higher for women who received intercessory prayer.

(d)

To determine

To explain why this is important.

Explanation of Solution

In this study it is mentioned that the women did not know that they were being prayed for or not while they were having IVF. This is important for a study to hide this because if the women were aware that they were being prayed for, they might unconsciously change their behavior, which could change the chance of a pregnancy. And this will directly affect the accuracy of the result of the researcher.