Problem 2. (20 Points) You are hired as a consultant by a company to assess whether two different production methods used to produce the same microprocessor display differences in terms of the lifespan of the microprocessor. Let X represent the random wvariable representing the lifespan of a microprocessor produced using method 1 and Y represent the random variable representing the lifespan of a microprocessor produced using method 2. Let mx represent the unknown median of X and my the unknwon median of Y. The company is interested in knowing if production method 1 produces microprocessors with a higher median compared to production method 2 (Hy : mx > my ). You collect data about the lifespan (measured in years) of 7 microprocessor produced with method 1 and 5 microprocessor produced with method 2, obtaining the following samples: z;: 12 13 8 7 9 14 10 y;i: 11 8 15 12 6 Perform a Wilcoxon's rank sum test to test the alternative hypothesis Hy : mx > my against the null hypothesis Hy : mx = my, given a significance level of a = 0.05