Question

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 $H_0:{\mu }_T-{\mu }_P=0$versus $H_a:{\mu }_T-{\mu }_P>0$, where ${\mu }_T$= 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 $\alpha =0.01$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 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

Short answer

Option(a) is correct answer. The power of test would be less than $80\%$

Step-by-step solution

Given information

We need to find the test power.

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 $80\%$.