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.

The two samples are independent. Use a 0.05 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.

(a) State the test used.

(b) Give a. State the null and alternate hypotheses.

(c) Find the sample test statistic.

(d) For the sign test, rank-sum test, and Spearman correlation coef­ficient test, fi­nd the P-value of the sample test statistic. For the runs test of randomness, ­find the critical values from Table 10 of Appendix II.

(e) Conclude the test and interpret the results in the context of the application

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With catalyst 1.6 3.2 2.9 4.4 3.7 2.5 1.1 1.8 3.8 4.2 4.1 Without catalyst 3.9 4.6 1.5 2.2 2.8 3.6 2.4 3.3 1.9 4.0 3.5 3.1