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.
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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.)
| Type | Score | Rank | ||
| sample 1 | 10 | 7 | ||
| sample 1 | 23 | 16 | ||
| sample 1 | 9 | 6 | ||
| sample 1 | 11 | 8 | ||
| sample 1 | 18 | 13 | ||
| sample 1 | 5 | 2 | ||
| sample 1 | 21 | 15 | ||
| sample 1 | 14 | 11 | ||
| sample 2 | 12 | 9 | ||
| sample 2 | 6 | 3 | ||
| sample 2 | 7 | 4 | ||
| sample 2 | 8 | 5 | ||
| sample 2 | 15 | 12 | ||
| sample 2 | 13 | 10 | ||
| sample 2 | 19 | 14 | ||
| sample 2 | 4 | 1 | ||
| sample size n1 = | 8 | sample 1 | ||
| sample size n2 = | 8 | sample 2 | ||
| Rank sum (R1)= | 78 | |||
| Rank sum (R2)= | 58 | |||
| test statistic =w1 =R1 = | 78 | |
| mean =μ=n1(n1+n2+1)/2= | 68 | |
| Variance σ2=n1n2(n1+n2+1)/12= | 90.67 | |
| σ=√n1n2(n1+n2+1)/12= | 9.522 | |
| z score =(w1-μ)/σ = | 1.05 | |
retain the null hypothesis.
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