Use the Mann-Whitney Table to find the critical values. For a left-tailed or two-tailed test, you will also need the relation
$\mathrm { M } _ { 1 - \mathrm { A } } = \mathrm { n } _ { \mathbf { 1 } } \left( \mathrm { n } _ { 1 } + \mathrm { n } _ { 2 } + 1 \right) - \mathrm { M } _ { \mathrm { A } } \text {. }$
-$\mathrm { n } _ { 1 } = 8 , \mathrm { n } _ { 2 } = 4$, significance level $= 0.01$, two-tailed test
A)39,65
B) 12,40
C) 38,66
D) 40,64

Question

Use the Mann-Whitney Table to find the critical values. For a left-tailed or two-tailed test, you will also need the relation
$\mathrm { M } _ { 1 - \mathrm { A } } = \mathrm { n } _ { \mathbf { 1 } } \left( \mathrm { n } _ { 1 } + \mathrm { n } _ { 2 } + 1 \right) - \mathrm { M } _ { \mathrm { A } } \text {. }$
-$\mathrm { n } _ { 1 } = 8 , \mathrm { n } _ { 2 } = 4$, significance level $= 0.01$, two-tailed test  
A)39,65
B) 12,40
C) 38,66
D) 40,64

Quizplus · Accepted Answer

For a two-tailed test at the 0.01 significance level with $n_1 = 8$ and $n_2 = 4$, we first find the critical value for $\alpha/2 = 0.005$ (since it's two-tailed) from the Mann-Whitney table. Assuming the table gives us a critical value of $M_A$ for $\alpha = 0.01$ for the smaller group (in this case, $n_2 = 4$), we then use the given formula to find the upper critical value. The correct critical values are 38 and 66, which are found by looking up the lower critical value in the table and calculating the upper critical value using the given formula.

Use the Mann-Whitney Table to Find the Critical Values - n1=8,n2=4\mathrm { n } _ { 1 } = 8 , \mathrm { n } _ { 2 } = 4n1​=8,n2​=4

Use the Mann-Whitney Table to Find the Critical Values - $\mathrm { n } _ { 1 } = 8 , \mathrm { n } _ { 2 } = 4$