The Mann-Whitney U test is a non-parametric alternative to the student's t-test and measures the likelihood that a randomly selected value from sample set 1 will be significantly different from a randomly selected value from sample set 2. When testing for a significant lowering in the value of a parameter in sample set 2, the U test counts the total number of occasions for which any value in set 2 is higher than any value in set 1. The null hypothesis can be rejected if the calculated U value so derived is less than or equal to a test statistic.

Use the Mann-Whitney U test to determine if protein precipitation has significantly reduced the concentration of Mg2+ ions in six independent samples of human blood plasma (see the data in Table 1 below and then answer all four questions a) to d)).

Table 1 Concentration of Mg2+ in ug/ml in human plasma prior to protein precipitation	Concentration of Mg2+ in ug/ml in in human plasma after protein precipitation
10.0	9.0
9.4	7.0
7.7	6.4
8.3	8.0
9.6	6.2
10.2	7.6

A. What are the benefits of using a non-parametric test such as the Mann- Whitney U test relative to a parametric test such as the student's t- test?

b) What is the null hypothesis for the protein precipitation treatment experiment?

c) What is the U statistic for the reduction in concentration of Mg2+ ions in the six samples of human plasma after protein precipitation?

d) Given that the test statistic for p = 0.05 is 7, determine if the protein precipitation treatment significantly reduced the concentration of Mg2+ ions at 95% confidence.