# A pharmaceutical company claims that its new drug helps lower blood pressure

August 30, 2017

uestion
A pharmaceutical company claims that its new drug helps lower blood pressure. The drug was
given to 50 patients in a clinical trial. Results from this trial showed that the drug decreased
mean systolic blood pressure by 1mmHg with a standard deviation of 5 mmHg. Let µ be the true
mean decrease in systolic blood pressure due to the new drug.
a. What is the probability of observing xx = 1 if µ =0
b. Since the results were not statistically significant at ? = 0.05, the company would not
receive approval from the FDA to market this drug. One of the researchers in this
company took STAT 3011 and remembered that the p-value could be improved (i.e.,
lowered) by increasing the sample size. So the company ran a second clinical trial with
the same blood pressure drug on 500 patients and once again observed that the drug
decreased mean systolic blood pressure by 1mmHg with a standard deviation of 5
mmHg. What is the probability of observing xx = 1 if µ = 0 in the second trial?
c. Why might the FDA be reluctant to approve the drug even if we rejected H0 at ?
0.01 in the second trial?

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