In a Wilcoxon rank sum test n₁ = 12, n₂ = 15 and the sum of R₁ = 108. The value of the test statistic for the normal approximation is: A)-1.23. B)-2.93. C)-108. D)108. E)15.

Question

Quizplus · Accepted Answer

The formula for the Wilcoxon rank sum test statistic is:

W = RS1U1B11S1U1B0 - nS1U1B11S1U1B0(nS1U1B11S1U1B0 + 1) / 2

For this problem, we have RS1U1B11S1U1B0 = 108 and nS1U1B11S1U1B0 = 12, so:

W = 108 - 12(12+1)/2 = 12

We also have nS1U1B12S1U1B0 = 15, so the other sample size is:

nS1U1B22S1U1B0 = nS1U1B11S1U1B0 + nS1U1B12S1U1B0 = 12 + 15 = 27

Since the sample sizes are both greater than 10 and the sum of the ranks is not tied, we can use the normal approximation to calculate the p-value of the test.

The mean of the Wilcoxon rank sum test statistic under the null hypothesis is:

E(W) = nS1U1B11S1U1B0nS1U1B12S1U1B0 / 2 = 12 * 15 / 2 = 90

The standard deviation of the Wilcoxon rank sum test statistic under the null hypothesis is:

SD(W) = sqrt(nS1U1B11S1U1B0nS1U1B12S1U1B0(nS1U1B11S1U1B0 + nS1U1B12S1U1B0 + 1) / 12)

= sqrt(12 * 15 * (12 + 15 + 1) / 12)

= sqrt(630)

So the test statistic for the normal approximation is:

Z = (W - E(W)) / SD(W)

= (12 - 90) / sqrt(630)

= -2.93

Therefore, the answer is B) -2.93.

In a Wilcoxon Rank Sum Test N1 = 12, N2

In a Wilcoxon Rank Sum Test N₁ = 12, N₂