Question

Chapter 13, Question 18. To address whether carotenoids influence immune system function, researchers gave ten individual finches supplemental carotenoids in their diet, and had 10 individuals that did not. All 20 birds were then measured using an assay that measures cell-mediated immunocompetence (PHA) as well as an assay that measures humoral immunity (SRBC). The data are given below. The researchers had independent reasons to believe that neither assay score would be normally distributed, so they preferred a nonparametric test.

Does PHA differ on average between the birds that received supplemental carotenoids and those that did not?

TREATMENT	PHA	SRBC
CAROT	1.311	2
CAROT	1.311	2
CAROT	1.460	3
CAROT	1.352	4
CAROT	1.491	5
CAROT	1.599	4
CAROT	1.653	8
CAROT	1.390	5
CAROT	1.779	7
CAROT	1.721	4
NO	1.454	4
NO	1.226	2
NO	1.198	3
NO	1.139	4
NO	1.277	3
NO	1.490	0
NO	0.912	3
NO	1.316	4
NO	1.234	2
NO	1.332	1

H0: No difference in median between groups.

HA: There is a difference in median between groups.

To begin, what is the value of U1 (assuming CAROT is group 1)?

What is the P-value?

Answer 1

H0: No difference in median between groups.

HA: There is a difference in median between groups.

Test statistic: Mann-Whitney U = 13.000

P-value=0.005

Conclusion: the p-value of Mann-Whitney U test is less than 0.05. Hence we reject null hypothesis and conclude that there is a difference in median between groups