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Researchers want to evaluate the effect of a natural product on reducing blood pressure. They plan to carry out a randomized experiment to compare the mean reduction in blood pressure of a treatment (natural product) group and a placebo group. Then they will use the data to perform a test of $H_0:{\mathrm{μ}}_T−{\mathrm{μ}}_P=0$versus $H_a:{\mathrm{μ}}_T−{\mathrm{μ}}_P>0$, where ${\mathrm{μ}}_T$= the true mean reduction in blood pressure when taking the natural product and μP = the true mean reduction in blood pressure when taking a placebo for subjects like the ones in the experiment. The researchers would like 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 twosample t test using $\mathrm{Î\pm }=0.01$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 the 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 $80\%$.

e. would vary depending on the standard deviation of the data

Step by step solution

01

Given information

We need to find the test power.

02

Simplify

According to the question, if a researcher wishes to discover a seven-point difference, he or she will require a power of $80$ percent.
Then, if a study wants to discover a five-point difference, we know that larger differences are easier to detect and hence have a higher power.
As a result, if the difference is reduced from $7$to $5$, the power is reduced as well, and the right answer is (a), implying that the test's power is less than $80\%$.

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