A professor has a teaching assistant record the amount of time (in minutes) that

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. Without With Microsoft Microsoft PowerPoint PowerPoint 11 12 23 19 13 10 21 18 14 Use the normal approximation for the Mann-Whitney Utest to analyze the data above. (Round your answer to two decimal places.) State whether to retain or reject the null hypothesis Assume alpha equal to 0.05.) O Retain the null hypothesis. O Reject the null hypothesis.

Explanation / 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

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

Ascending order of the give n data is

Rank table as show in the below

With microsoft

PPT

Without microsoft

PPT

  Total R1 =80Total R2 =56

now test statstic here n=8 as 8 rows

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

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

=20

u2 =   n1n2 + n2(n2+1) /2 -R2

= 8* 8+ (8 *9 ) /2 - 56

= 44

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

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

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