Problem 4. (25 points, 5 parts) Erin and Tabish are operations engineers for iStow Co._. a warehousing solutions company. iS'tow uses Kiva Robots to bring shelves to associates who then stow items in the shelves, before the robots whisk them away. Erin and Tabish have designed a new process flow that they hope improves upon the old system. They have run a pilot study in order to, hopefully. demonstrate that their new process is better. Specically, they hope that the average number of items stowed per shift increases. The le \"iStow.xlsx" contains the results of the pilot study. For the pilot, 30 associates were chosen. The same ssociates were used to test both the Old and the New processes. The numbers given are, for each associate, the average number of items stowed per shift under the corresponding processes. In the analysis below, if a standard deviation estimate is required, assume that the population standard deviation is the same for both the Old and the New processes. Use a 5% level of signicance. a) Clearly state both the null and alternative hypotheses. b) Erin and Tabish sampled 3'3 associates so that the Central Limit Theorem (CLT) would apply to their analysis. In addition to having a large enough sample, what other assumptions are required for the CLT to apply? c} Calculate the test statistic. d) Calculate the pvalue. e) Is there enough evidence to conclude that the New process is better? Old New 331.4 301.6 2 314.8 310.7 332.8 325.9 4 324.6 368.4 LA 276.9 350.2 320.3 303.3 284.9 393.9 339.4 311 9 330.1 321.8 10 307.5 268.6 11 286.7 342.7 12 278.9 335.3 13 288.3 352.9 14 316 320.4 15 318.7 321.1 16 274 322.2 17 359 330 18 302.4 331.8 19 311.4 395.6 20 282.4 313.4 21 340.4 323.4 22 309.7 356.1 23 300.2 255.6 24 316.6 310.9 25 298.1 328.6 26 326.8 290.6 27 341.1 318.9 28 273.9 279.8 29 341.4 365.7 30 286.7 262