Complete Table 2 and calculate the Mann-Whitney $U\,$ value for the results of Elena's investigation.

Use the following formulas for the Mann-Whitney $U\,$ test:

U_a = n_a n_b + \frac{n_a(n_a + 1)}{2} - R_a

U_b = n_a n_b + \frac{n_b(n_b + 1)}{2} - R_b

where:

$n_a\,$ and $n_b\,$ are the sample sizes of Group A and Group B respectively ( $n_a = 10, n_b = 10$ )
$R_a\,$ and $R_b\,$ are the sum of the ranks for Group A and Group B respectively
the final test statistic $U\,$ is the smaller of $U_a\,$ and $U_b\,$

Table 2:

Condition A: Silent study room		Condition B: Lyrical background music
Reading score (out of 15)	Rank	Reading score (out of 15)	Rank
12	14	8	5
14	18.5	10	9.5
11	11.5	9	7.5
13	16.5	8	5
15	20	9	7.5
12	14	12	14
11	11.5	7	3
10	9.5	8	5
13	16.5	6	2
14	18.5	5	1
Total		Total

Complete Table 2 and calculate the Mann-Whitney $U\,$ value for the results of Elena's investigation.

Use the following formulas for the Mann-Whitney $U\,$ test:

U_a = n_a n_b + \frac{n_a(n_a + 1)}{2} - R_a

U_b = n_a n_b + \frac{n_b(n_b + 1)}{2} - R_b

where:

$n_a\,$ and $n_b\,$ are the sample sizes of Group A and Group B respectively ( $n_a = 10, n_b = 10$ )
$R_a\,$ and $R_b\,$ are the sum of the ranks for Group A and Group B respectively
the final test statistic $U\,$ is the smaller of $U_a\,$ and $U_b\,$

Table 2:

Condition A: Silent study room		Condition B: Lyrical background music
Reading score (out of 15)	Rank	Reading score (out of 15)	Rank
12	14	8	5
14	18.5	10	9.5
11	11.5	9	7.5
13	16.5	8	5
15	20	9	7.5
12	14	12	14
11	11.5	7	3
10	9.5	8	5
13	16.5	6	2
14	18.5	5	1
Total		Total

Methods

Methods Questions