Question

5) A research group has collected information about response times in humans. They want to compare the response times of people early in the workday with response times of participants late in the workday. The response times appear below. Since response time over the population is not normally distributed they use a Mann-Whitney U test. Compute U for these data and evaluate whether there is a significant difference between groups.

Early day 300 275 328 400 280 335 310

Late in the day 325 310 295 375 380 410 390

Answer 1

Early day	Ranking	Late in the day	Ranking
275	1	295	3
280	2	310	5.5
300	4	325	7
310	5.5	375	10
328	8	380	11
335	9	390	12
400	13	410	14
n1 = 7	= 42.5	n2 = 7	= 62.5

If the response time of people early day in the work and late in the day of the work both are same. Then this Hypothesis is assumed as H1.

If the response time of people early day in the work and late in the day of the work both are not same. Then this Hypothesis is assumed as H2.

+ = 42.5 + 62.5 = 105

  , (where n= n1+n2)

Hence, the above given data follows the Mann-Whitney U test,

From Mann-Whitney U test

So U = Min (U1,U2) = Min (34.5,14.5)

Therefore U = 14.5

Then there is a significant difference between groups.  which is equal to

14.5 - 14.5 = 0.05