Question

IX 3 In a certain management study, 15 randomly selected managers were found to spend a mean of 2.40 hours each day on paperwork with a standard deviation of 1.30 hours. a. Construct a 90% Confidence Interval for the mean time spent on paperwork by all managers. b. State the meaning of the interval in the context of the problem. X Use the given data to construct a confidence interval at the requested level: x = 125, n = 317, confidence level 95% (Hint: Refer to #Va and VI from Test 3.)

Answer 1

IX. Solution: The prouded information_is_ed follows Sample size DES sample... meant 2.40 Sample standard deviation is: 1:30 confidence level - KE6 go X = alo. The number of degrees of freedom are df = +1 = 15-15 14; and the significance level is a = 0.10 Based on the provided information the critical t-value for x = 0.10 and df = 14 degrees of freedom is te= .1.761 G) The go% confidence for the population mean time spent time spent on paperwork by call managed is consputed cis. cis folloross! X - texs un Xitexs un -(2:40 2.40-1.76111:30 vis 2-40-2 1.7610 1:30 VTS 2.40-0.59). 2.4040.5912 CI= 1.80g, 2.gg 1) Therefore the go% confidence intewal is CI= (1.809; 2.991)

state the meaning of the internal in the context of the problema The gol confidence intewal for the mean time spent paperwork by all managens is (1.809, 2.991 which indicates that go% confident that the the population mean time sproti on paperworks by managers is contained by the internal (1.809, Ž.991) we are all X. Solution. The provided io formation is as followers Sample size nr 317 number of favorable X = 125 sample propostica pax 125 = 0.394 Cases 317 The critical value for x=0.05 is ze=2r af 1.96 - Then some spending confidence in temal is computed as followess'; CIE CI fez zpCp), PA 20 PC- p) 501394-1-960.394(1-0,394), 0,394-43.96.40.394(1-0.394). 0139-1.96 for 317 317 (0.394 -0.054, 0:394 10.054) CI. fo: 340, 0.448 Therefore 95% confidence internal is (0.340, 8.448