Question

A professor has a teaching assistant record the amount of time (in minutes) that a sample of 16 students engaged in an active discussion. The assistant observed 8 students in a class who used a slide show presentation and 8 students in a class who did not use a slide show presentation.

With Microsoft PowerPoint	Without Microsoft PowerPoint
11	19
10	8
18	12
6	9
5	23
4	7
13	14
15	21

Use the normal approximation for the Mann-Whitney U test to analyze the data above. (Round your answer to two decimal places.)
z =

Answer 1

Answer:

For the study of the performance of the studies in two different conditions we have to conduct Mann-Whitney U test

The null ad alternative hypothesis are

H_o: f(x) =f(y) The performance of two independent students are equal

Ascending order of the give n data is

rank	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
data	4	5	6	7	8	9	10	11	12	13	14	15	18	19	21	23

Rank table as show in the below

With microsoft PPT	Rank1	Without microsoft PPT	Rank2
11	8	19	14
10	7	8	5
18	13	12	9
6	3	9	6
5	2	23	16
4	1	7	4
13	10	14	11
13	10	21	15

  Total R1 =54 Total R2 =80

now test statstic here n=8 as 8 rows

u1 = n1n2 + n2(n2+1) /2 -R1

= 8* 8+ (8 *9 ) /2 - 54

=46

u2 =   n1n2 + n2(n2+1) /2 -R2

= 8* 8+ (8 *9 ) /2 - 80

= 20

m = E(U)= n1*n2/2 = 8*8 /2 = 32

var(u) =  n1n2 + n2(n2+1) / 12 =

= 90.667

z= u-e(u) / sqrt var(u) = 20-32 /sqrt(90.667)

= -1.260 so here we retain the null hypothesis

za/2=0.005 = z0.005/2 = 1.96 from z value table

so z= -1.26> 1.96

we accept null hypothesis and retain it

NOTE:

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