using mannwhitney or Wilcoxon test Two independent samples r

using mann-whitney or Wilcoxon test

Two independent samples ranking method

In a controlled environment laboratory, 10 men and 10 women were tested to determine the room temperature they found to be the most comfortable. The results were as follows. Assuming that these temperatures resemble a random sample from their respective populations, is the average comfortable temperature the same for men and women?

Solution

N Median
C2 10 74.500
C3 10 78.000

Point estimate for ETA1-ETA2 is -3.000
95.5 Percent CI for ETA1-ETA2 is (-5.001,-0.999)
W = 68.0
Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.0058
The test is significant at 0.0055 (adjusted for ties)

so here p-value for mann-whitney is .0055<.05 so we clame that the teo samples are not identical