Question

4. Suppose you are interested in the effect of an experimental drug on blood pressure. Blood pressures in mmHg are measured before and after treatment from a random sample of 15 participants. The following data result: Pre 134 103 116 113 124 120 128 122 123 108 134 108 111 125 134 Post 134 106 110 115 122 126 130 118 125 110 138 111 115 125 130 a) b) (1 mark) Find a 95% confidence interval for the true mean of the difference in blood pressures (Pre-Post). Include your command and output. (1 mark) Give the command and output to test if there is any effect of the experimental drug on blood pressure. (1 mark) What is the observed value of the test statistic? (1 mark) What is the distribution of the test statistic (with parameter if any) under Ho? c) d) e) (1 mark) What is the p-value for our test?

Answer 1

Solution

we will find the solution using R

> pre=c(134, 103, 116, 113, 124,120,128, 122,123,108, 134, 108, 111, 125, 134)
> post=c(134,106,110,115,122,126,130,118,125,110,138,111,115,125,130)
> b=t.test(pre,post,paired = T)
> b

   Paired t-test

data: pre and post
t = -0.90417, df = 14, p-value = 0.3812
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-2.69769 1.09769
sample estimates:
mean of the differences
-0.8

> c=b$statistic
> c
t
-0.9041672
> # d = t -distribution with 14 degrees of freedom
> c=t.test(pre,post,paired = T)
> e=b$p.value
> e
[1] 0.3812024
> a=b$conf.int
> a
[1] -2.69769 1.09769
attr(,"conf.level")
[1] 0.95

conclusion : Since the p-value = 0.3812024 > 0.05 level of significance so accept the null hypothesis and conclude that there is no effect of experimental drug on blood pressure.