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.

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

State whether to retain or reject the null hypothesis. (Assume alpha equal to 0.05.)

Retain the null hypothesis.Reject the null hypothesis.   

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

Explanation / Answer

H0 :1 = 2

Ha : 1 > 2

Here the mann whiteny rank table is given below

Here R1 =  sum of Ranks = 16 + 10 + 6 + 9 + 14 + 15 + 2 + 13 = 85

U1  = R1 - n1(n2+1)/2 = 85 - 8 * 9/2 = 49

R2 =  sum of Ranks = 5 + 1 + 3 + 4 + 12 + 11 + 8 + 7 = 51

U1  = R1 - n1(n2+1)/2 = 51 - 8 * 9/2 = 15

Here the Test statistic

U = min (U1, U2 ) = 15

Here,

Z = (U - mu)/U

where mU = n1 n2/2 = (8*8)/2 = 32

U = sqrt [n1n2(n1 + n2 + 1)/12] = sqrt [8 * 8* 17/12] = 9.522

Z =  (U - mu)/U = (15 - 32)/9.522 = -1.73

p - value = 0.042

At alpha = 0.05, we reject the null hypothesis .

With Microsoft Powerpoint Without Microsoft Powerpoint Combined Column Combined Rank With Microsoft Powerpoint Without Microsoft Powerpoint 23 8 23 16 16 5 13 4 13 10 10 1 9 6 9 6 6 3 12 7 12 9 9 4 19 15 19 14 14 12 21 14 21 15 15 11 5 11 5 2 2 8 18 10 18 13 13 7 8 5 4 1 6 3 7 4 15 12 14 11 11 8 10 7

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