Question

It has been shown that levels of beta-endorphin in the blood are elevated by emotional stress. For 19 patients scheduled to undergo surgery, blood samples were taken twice: (a) 12-14 hours before surgery and (b) 10 minutes before surgery. Beta-endorphin levels were measured in fmol/ml.

Assuming the symmetry of the distributions, determine if there is a significant increase in beta-endorphin levels immediately before surgery.

(a)	10.0	6.5	8.0	12.0	5.0	11.5	5.0	3.5	7.5	5.8
	4.7	8.0	7.0	17.0	8.8	17.0	15.0	4.4	2.0
(b)	6.5	14.0	13.5	18.0	14.5	9.0	18.0	42.0	7.5	6.0
	15.0	12.0	52.0	20.0	16.0	15.0	11.5	2.5	2.0

Suppose that you mistakenly believed that the data sets were independent samples taken from two different populations: blood samples were taken 12-14 hours before surgery from one set of 19 patients and a different set of 19 patients from whom the blood was drawn 10 minutes before surgery.

Carry out the t test and determine whether you would have found that female dementia patients who were given bright light and melatonin would have a significantly higher subjective scores for well-being.

Explain the cause of any differences in your results when compared to the previous problem.

Answer 1

R code:

x1=c(10.0,6.5,8.0,12.0,5.0,11.5,5.0,3.5,7.5,5.8,4.7,8.0,7.0,17.0,8.8,17.0,15.0,
4.4,2.0)
x2=c(6.5,14.0,13.5,18.0,14.5,9.0,18.0,42.0,7.5,6.0,15.0,12.0,52.0,20.0,16.0,15.0,
11.5,2.5,2.0)
t.test(x1, x2, paired=TRUE,alternative ="less")

Output:

Paired t-test

data: x1 and x2
t = -2.3703, df = 18, p-value = 0.01457
alternative hypothesis: true difference in means is less than 0
95 percent confidence interval:
-Inf -1.925592
sample estimates:
mean of the differences
-7.173684

Since p-value = 0.01457<0.05, there is significant evidence that  female dementia patients who were given bright light and melatonin would have a significantly higher subjective scores for well-being.