A Mann-Whitney U test was performed to determine if there were differences in the average compute time for Dallas residents versus Atlanta residents.The travel time for 22 commuters in Dallas was compared to the travel time for 28 commuters in Atlanta.The U statistic was calculated to be 58.0 based on the sample sizes of 22 and 28.What is the z value for this test?
A) 51.17
B) 308
C) 0.117
D) -4.88
E) -2.44

Question

Quizplus · Accepted Answer

To find the z value, use the formula:

z = (U - μ) / σ

where: 
- U is the calculated U statistic 
- μ is the mean of the null hypothesis (which is n1 * n2 / 2, where n1 and n2 are the sample sizes) 
- σ is the standard deviation of the null hypothesis (which is sqrt(n1 * n2 * (n1+n2+1) / 12))

Plugging in the values, we get:

z = (58 - (22*28/2)) / sqrt(22*28*(22+28+1)/12) 
z = -4.88

Therefore, the answer is D.

A Mann-Whitney U Test Was Performed to Determine If There