Book edition 4th

Author(s) David Moore,Daren Starnes,Dan Yates

Pages 809 pages

ISBN 9781319113339

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Short Answer

Researchers are interested in evaluating the effect of a natural product on reducing blood pressure. This will be done by comparing the mean reduction in blood pressure of a treatment (natural product) group and a placebo group using a two-sample t-test. The researchers would like to be able to detect whether the natural product reduces blood pressure by at least $7$ points more, on average than the placebo. If groups of size $50$ are used in the experiment, a two-sample t-test using role="math" localid="1650436089340" $α = 0.01$ will have a power of $80 %$ to detect a $7$ -point difference in mean blood pressure reduction. If the researchers want to be able to detect a $5$ -point difference instead, then the power of test
(a) would be less than $80 %$ .
(b) would be greater than $80 %$ .
(c) would still be $80 %$ .
(d) could be either less than or greater than $80 %$ , depending on whether the natural product is effective.
(e) would vary depending on the standard deviation of the data.

If the researchers want to be able to detect a $5$ -point difference instead, then the power of test is option (a) would be less than $80 %$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

The size of group is $50$

$α = 0.01$

Power $= 80 %$

Step 2: Explanation

The larger difference is easier to detect and thus has a higher power.

We'd like to see how effective a natural product is at lowering blood pressure. As a result, the smaller the difference between $μ_{1} - μ_{2}$

the better.

Hence $μ_{1 -} μ_{2} \geq 7$ if the test's power is $80 %$ for alternative hypothesis.

Then, For alternate hypothesis, $μ_{1 -} μ_{2} < 5$ the test's power will be greater than $80 % .$

Since the difference is decreased from $7$ to $5$ , the power will also decrease and thus the correct answer is (a).

Step 3: Incorrect Answer

Since the difference is decrease from 7 to 5, power would not be greater than 80%. It cannot depending on the standard deviation of the data. Therefore option b, c, d and e are incorrect answers.

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