Question

Question 2: The efficacies of two drugs, X and Y were evaluated in two groups of mice (Group C, Group D). The outcome was the concentration of the drug in the plasma after giving the mice drugs (through drinking water) for 24 hours. The data were summarized below.

Group C	Group D
3	10
4	7
6	11
6	10
7	9
5	11
6	12
5	14
8	8
9	13

Question 2A. At the significance level of 0.05, are the drug concentrations in Group C and Group D different? Using Mann-Whitney U test here.

Answer 1

here,we are doing  Mann-Whitney U test.

hypothesis:-

The two populations are equal versus

The two populations are not equal.

necessary calculation table:-

we order the data from smallest to largest by combining  and assigning ranks from 1 to 20, as follows.

		Total Sample (Ordered Smallest to Largest)		Ranks
group C	group D	group C	group D	group C	group D
3	10	3		1
4	7	4		2
6	11	5		3.5
6	10	5		3.5
7	9	6		6
5	11	6		6
6	12	6		6
5	14	7	7	8.5	8.5
8	8	8	8	10.5	10.5
9	13	9	9	12.5	12.5
			10		14.5
			10		14.5
			11		16.5
			11		16.5
			12		18
			13		19
			14		20
				sum=59.5	sum =150.5

the sum of rank of group C be:-

the sum of rank of group D be:-

The test statistic (U) and is the smaller of U_c and U_{d :-}

test statistic(U) = min (95.5 , 4.5) = 4.5

critical value of U = 23

[ from Mann Whitney U table, for = 10, =10 , alpha= 0.05 , both tailed test]

decision:-

we reject the null hypothesis.

we conclude that,

there is  statistically significant evidence at α =0.05 to show that the drug concentrations in Group C and Group D different.

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