[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 year spent on research were presumed to be 30 and 60 days, respectively. Find the sample size needed for proportional allocation to estimate the population mean with the S.E. of the estimator not exceeding 10 and its allocation for the two groups. [5] Question 4 [5] 4.1. For the survey conducted by Klein Associates, Inc. on 2000 lawyers on sexual advances in the office, find the sample sizes needed for the following requirements: (a) The standard errors for women and men should not exceed 4 and 1%, respectively, and (b) the S.E. for the difference of the percentages for women and men should not exceed 3%. [5] [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 year spent on research were presumed to be 30 and 60 days, respectively. Find the sample size needed for proportional allocation to estimate the population mean with the S.E. of the estimator not exceeding 10 and its allocation for the two groups. [5] Question 4 [5] 4.1. For the survey conducted by Klein Associates, Inc. on 2000 lawyers on sexual advances in the office, find the sample sizes needed for the following requirements: (a) The standard errors for women and men should not exceed 4 and 1%, respectively, and (b) the S.E. for the difference of the percentages for women and men should not exceed 3%. [5]