In: Statistics and Probability
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 |
---|---|
6 | 4 |
11 | 14 |
10 | 18 |
7 | 21 |
19 | 8 |
9 | 12 |
15 | 13 |
5 | 23 |
Use the normal approximation for the Mann-Whitney U
test to analyze the data above. (Round your answer to two decimal
places.)
z =
Solutions:-
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 | 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 shown in the below:
With Microsoft PPT | Rank-1 | With Microsoft PPT | Rank-2 |
6 | 3 | 4 | 1 |
11 | 8 | 14 | 11 |
10 | 7 | 18 | 13 |
7 | 4 | 21 | 15 |
19 | 14 | 8 | 5 |
9 | 6 | 12 | 9 |
15 | 12 | 13 | 10 |
5 | 2 | 23 | 23 |
Total R1 = 56
Total R2 = 87
Now test statistics here n = 8 as 8 rows
u1 = n1n2 + n2(n2+1) / 2 - R1
= 8*8 + (8*9) / 2-56
= 44
u2 = n1n2 + n2(n2 + 1) / 2 - R2
= 8*8 + (8*9) / 2 - 87
= 13
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)
= 13 - 32 / sqrt(90.667)
= - 1.9995
Z ~= -2.00
So here we retain the null hypothesis.
Za/2 = 0.005 = Z0.005/2 = 1.96 from z table
So
Z = -2.00 > 1.96
we accept null hypothesis and retain it.
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