Question 2 [20] 2.1. Among the 100 computer corporations in a region, average of the employee sizes for the largest 10 and smallest 10 corporations were known to be 300 and 100, respectively. For a sample of 20 from the remaining 80 corporations, the mean and standard deviation were 250 and 110, respectively. For the total employee size of the 80 corporations, find the (a) estimate, (b) the S.E. of the estimate, and (c) the 95% confidence limits. (10) 2.2. Select all the 20 samples of size three from the population of six students in Table 2.1, below without replacement. From each sample, find the 95% confidence limits for the population mean of the math scores with the known population variance and its estimates; use the normal deviate Z = 1.96 in both cases. (a) For both the procedures, find the proportion of the confidence intervals enclosing the actual population mean, that is, the coverage probability. (b) Compare the average of the confidence widths obtained with the estimates of variance with the exact width for the case of known variance. Table 2.1. SAT verbal and math scores. 520 Total Student Verbal Math i X; yi 1 670 2 690 720 3 500 650 4 580 720 5 530 560 6 480 700 3300 4020 Mean 550 670 Variance 02 4866.67 3066.67 S 5840 3680 S 76. 60.66 C.V. (%) 13.89 9.05 Activate Windows C.V. = coefficient of variation. Go to Settings to activate Windows. [10] Question 3 [5] 3.1. For the 200 managers and 800 engineers of a corporation, the standard deviations of the number of days a vear spent on research were presumed to be 30 and 60 days respectively Find the