Question

A medical researcher is studying the effects of a drug on blood pressure. Subjects in the study have their blood pressure taken at the beginning of the study. After being on the medication for 4 weeks, their blood pressure is taken again. The change in blood pressure is recorded and used in doing the hypothesis test. Change: Final Blood Pressure - Initial Blood Pressure The researcher wants to know if there is evidence that the drug increases blood pressure. At the end of 4 weeks, 32 subjects in the study had an average change in blood pressure of 2.5 with a standard deviation of 4.8. Find the p -value for the hypothesis test.

Answer 1

Answer:

The p -value for the hypothesis test is 0.003.

Step-by-step explanation:

In this case, a paired t-test would be used to determine whether the drug  increases blood pressure.

The hypothesis can be defined as follows:

H₀: The drug has no effect on blood pressure, i.e. d = 0.

Hₐ: The drug increases blood pressure, i.e. d > 0.

The information provided is:

$n=32\\\bar d=2.5\\S_{d}=4.8$

The test statistic is:

$t=\frac{\bar d}{S_{d}/\sqrt{n}}$

  $=\frac{2.5}{4.8/\sqrt{32}}\\\\=2.9463\\\\\approx 2.95$

The degrees of freedom of the test is:

$df=n-1=32-1=31$

The p-value of the test is:

$p-value=P(t_{31}>2.95)=0.003$

*Use a t-table.

Thus, the p -value for the hypothesis test is 0.003.