Question

A medical researcher wants to examine the relationship of the blood pressure of patients before and after a procedure. She takes a sample of 27 people and measures their blood pressure before undergoing the procedure. Afterwards, she takes the same sample of people and measures their blood pressure again. The researcher wants to test if the blood pressure measurements after the procedure are less than the blood pressure measurements before the procedure and, thus, the hypotheses are as follows: Null Hypothesis: μ_D ≥ 0, Alternative Hypothesis: μ_D < 0. If the average difference between the before and after blood pressures (calculated as after - before) is -3.85 with a standard deviation of 12.47, what is the test statistic and p-value?

Question 11 options:

1)	Test Statistic: -1.604, P-Value: 0.06

2)	Test Statistic: -1.604, P-Value: 0.94

3)	Test Statistic: 1.604, P-Value: 0.06

4)	Test Statistic: 1.604, P-Value: 0.94

5)	Test Statistic: -1.604, P-Value: 0.12

Answer 1

Solution:

Given in the question

No. Of sample = 27

Null Hypothesis H0: D >=0

Alternate hypothesis Ha: D<0

Average difference between the before and after blod pressure = -3.85

Standard deviation = 12.47

So test stat value can be calculated as

Test stat = (Sample average -Population average)/sample standard deviation/sqrt(n) = (-3.85-0)/12.47/sqrt(27) = -3.85/2.3998 = -1.604

Here degree of freedom = No. Of sample -1 = 27-1 = 26 and this is left tailed and one tailed test so p-value can be found from t table

P-value = 0.06

So it's answer is A. I.e. test stat = -1.604 and p-value = 0.06