In the production of synthetic motor lubricant from coal, a new catalyst has been discovered that seems to affect the viscosity index of the lubricant. In an experiment consisting of 23 production runs, 11 used the new catalyst and 12 did not. After each production run, the viscosity index of the lubricant was determined to be as follows. With catalyst 3.2 2.7 2.3 3.7 2.6 3.8 3.3 2.4 3.1 3.0 1.3
Without catalyst 1.4 3.9 2.1 1.9 1.8 1.2 1.7 2.8 3.5 4.1 4.3 1.5

The two samples are independent. Use a 0.01 level of significance to test the null hypothesis that the viscosity index is unchanged by the catalyst against the alternate hypothesis that the viscosity index has changed.

Required:
a. Find the sample test statistic. (Use 2 decimal places.)
b. For the sign test, rank-sum test, and Spearman correlation coefficient test, find the P-value of the sample test statistic.