Question

4. A question of medical interest is whether jogging leads to a reduction in systolic blood pressure. To learn about this question, eight nonjogging volunteers have agreed to begin a 1-month jogging program. At the end of the month their blood pressures were determined and compared with earlier values, with the following data resulting:

5. 	1	2	3	4	5	6	7	8
   Blood pressure before	134	122	118	130	144	125	127	133
   Blood pressure after	130	120	123	127	138	121	132	135

   1. (a) Suppose you want to see if these data are significant enough to prove that jogging for 1 month will tend to reduce the systolic blood pressure. Give the null and alternative hypotheses.

   2. (b) Do the data prove the hypothesis in (a) at the 5 percent level of significance?

   3. (c) Do the data prove that the hypothesis is false?

   4. (d) How would you present the results of this experiment to a medical

      person who is not trained in statistics?

Answer 1

a) Claim : We need to test if  jogging for 1 month will tend to reduce the systolic blood pressure.

The hypothesis are,

H0: = 0 v/s H1: < 0

b) The test statistic is,

Before	After	d = After - Before
134	130	-4
122	120	-2
118	123	5
130	127	-3
144	138	-6
125	121	-4
127	132	5
133	135	2

From data we get : n = 8, =  -0.875, = 4.291

So,

= -0.577

df = n-1 = 8-1 = 7 , = 0.05

The critical value =

Here calculated value of t < critical value of t

Hence we failed to reject null hypothesis.

Conclusion : At the 5% of significance, there are enough evidence to prove the null hypothesis.

c) Data does not prove that hypothesis is false.

d) A person who is not trained in statistic, can conclude that jogging for 1 month will tend to reduce the systolic blood pressure.