A Mann-Whitney U test was performed to determine if there were differences in the cost of tuition at a Texas state university versus an Oklahoma state university.The total cost,including room,board,and books for 24 freshman attending a Texas university were computed and compared to the total cost for 20 Oklahoma state university students.The U statistic was calculated to be 38.78 based on the sample sizes of 24 and 20.What is the z value for this test?
A) 0.133
B) -4.74
C) 240
D) 42.43
E) 8.75

Question

Quizplus · Accepted Answer

The U statistic is used to calculate the z value. The formula for z is z = (U - μ)/σ, where μ is the expected value of U under the null hypothesis and σ is the standard deviation of U. In this case, since the null hypothesis is that there is no difference in cost between the two universities, μ is (24*20)/2 = 240, and σ is sqrt[(24+20)*(24*20/2)/12] = 42.43. Therefore, z = (38.78 - 240)/42.43 = -4.74. Choice B is the correct answer.

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