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A quality control department of a battery company is testing the lifetime of two types of button cell produced by two production lines: a traditional line and a new line. The default lifetime of the battery is 760 days. 31 cells produced by the traditional line (Column Traditional Line") and 26 cells by the new line (Column New Line") are tested and the predicted lifetime are shown in sheet problem 2. Denote X and Y as the random variable of lifetime for the cells by traditional line and the new line, respectively. Answer the following questions. M Traditional Line New Line New Line Test 2 1 765.2630005 714.7529907 702.3854449 2 771.6090088 843.0430298 835.3060294 3 863.5139771 696.0969849 696.757949 4 709,0510254 723.5079956 722.6470963 s 823.6630249 731.0599976 720.0708534 766.598999 726.2689819 723.122232 7 7 755.1279907 737.3120117 727.1712066 8 739.5219727 646.7329712 643.6007504 838.763000S 752.6970215 748.8011459 10 785.3599854 751.2860107 751.9694925 11 766.7949829 751.1119995 745.5403403 12 7692139893 729.7219849 722.2559325 13 670.6450195 724.9169922 721.533554 14 793.927002 819.371 818.9519308 15 834.5900269 719.2990112 718.2677093 16 806.7260132 742.5289917 737.7185721 17 715.8880005 745.6749878 733.0061698 18 832.4229736 696.2579956 683.1905428 19 816.5540161 712.0819702 705.5008051 20 766 6110229 787.7609863 775.795389 21 803.9000244 764.8189697 765.508369 22 768.539978 734.0440063 736.418139 23 791.6560059 682.1040029 681.5409487 24 676.473999 751.8729858 746.9151233 25 713,6640015 728.0319824 721.6974668 26 755.6439819 738.427002 732.4564699 27 691.7709961 28 717.1859741 29 713.8579712 30 771.7609863 31 665.7550049 (a). Find the sample mean and sample standard deviation of the lifetime of the cells produced by each line. Construct the 95 percent two-sided confidence interval for the population mean of X and Y. (b). Denote Ux as the population mean of X. Use the sample mean and sample standard deviation of the cells by the traditional line, test the following hypothesis. What is the p-value for this hypothesis test? Given a = 0.10. Ho: Ux = 760 versus Hi: Ux # 760 (c). A test for a cell produced by the traditional line has a lifetime 740 days. If we need to construct a one-sided confidence interval (lower bound, co) in which 740 is included, what is the smallest value of the confidence level 1-a? (d). Per the regulation of their manufacturer, the population standard deviation of both the traditional line and new line is 45. Please construct the 99 percent two-sided confidence interval of X and Y, respectively. (e). Assume a new lifetime test is conducted again for the 26 cells by the new line to validate if the new line is qualified to produce. The testing results are shown in column New Line Test 2. Denote Z as the random variable for the new test of new line and uz is the mean. Di = Y; Zi is the difference from the paired observations for cell j. We thus treat D as a new random variable and up is the population mean of D