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Q. 10

Expert-verifiedFound in: Page 666

Book edition
4th

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

Pages
809 pages

ISBN
9781319113339

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" $\alpha =0.01$ 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 $80\%$.

The size of group is $50$

$\alpha =0.01$

Power $=80\%$

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 ${\mu}_{1}-{\mu}_{2}$

the better.

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

Then, For alternate hypothesis, ${\mu}_{1-}{\mu}_{2}<5$ 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).

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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