In immune.xlsx, some individuals received a treatment of carotenoids (CAROT) and some received no treatment (NO). Carotenoids belong to a class of molecules called isoprenoids, many of them are...

In immune.xlsx, some individuals received a treatment of carotenoids (CAROT) and some received no treatment (NO). Carotenoids belong to a class of molecules called isoprenoids, many of them are antioxidants and some of them are vitamins such as vitamin A and its precursor beta-carotene, which is found in carrots.  Because of the antioxidant properties of carotenoids the purpose of the study was to check if they have any effect on immunity.  The column PHA gives quantitative measuremenst of cell-mediated immunity and the column SRBC gives quantitative measurements of humoral immunity.  This is clearly a two-sample (non-paired) design.  Therefore, you need to perform a Mann-Whitney-U test to check for differences. Bear in minds that rank assignments in Excel can be quite tricky and, therefore, if you need to do a Mann-Whitney rank assignment it is probably best to do this by hand.

1) What is the rank sum of the SRBC data of the individuals, which received carotenoids and rank sum of the individuals which received no treatment?

2) What is the U1 of the SRBC data of the individuals, which received carotenoids and U2 which received no treatment?

3) What is the P-value of a two-tailed Mann-Whitney U test on the SRBC data?