Question

Native American (#1) [8.50, 9.48, 8.65]

Caucasian (#2) [8.27, 8.20, 8.25, 8.14]

Determine whether the Native Americans have higher MSCE using the Wilcoxon rank-sum test.

Answer 1

Here,we have to test following null and alternative hypotheses:

H0​: MSCENA = MSCEC vs

Ha​: MSCENA > MSCEC

First, We have to sort the combined data set into ascending order,

Now, we have to rank the observations.

The sum of the ranks for the Native American group is,

WNA ​= 5 + 6 + 7 = 18

and the sum of the ranks for the Caucasian group is,

WC = 1 + 2 + 3 + 4 = 10

Since, the Native American MSCE values in the data tend to be higher,

=> the test statistic is W = WNA = 18.

Testing rule:

At 0.05% level of significance, for sample size 7, the critical value for the type of alternative hypothesis is 3(value from statistical table) i.e. the null hypothesis is rejected if W 3.

Decision:

Since in this case W = 18 > 3, there is not enough evidence to reject null hypothesis, at the 0.05 significance level.