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Given:

\(\begin{array}{l}m = 5\\n = 5\\{H_0}:{\mu _1} = {\mu _2}\\{H_a}:{\mu _1} > {\mu _2}\\\alpha = 0.05\end{array}\)

Determine the rank of every data value. The smallest value receives the rank l, the second smallest value receives the rank 2, the third smallest value receives the rank 3, and so on.

If multiple data values have the same value, then their rank is the average of the corresponding ranks.

\({{\rm{W}}_1}\)is the sum of the ranks in the smaller sample:

\({\rm{w = 38}}\)

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme, assuming that the null hypothesis is true.
The P-value is the number (or interval) in the column\({P_0}(W \ge c)\)of the Wilcoxon rank-sum test table in the appendix that contains the w-value in the row\(m = 5,n = 5,c = 38\):

\(0.008 < P < 0.028\)

If the probability (P-value) is less than the significant level\(\alpha \), then reject the null hypothesis:

\(P < 0.05 \Rightarrow {\rm{ Reject }}{H_0}\).