Question

(1 point) The purpose of this question is to compare the variability of 21 and 22 with the variability of (71 22). (a) Suppose the first sample of 100 observations is selected from a population with mean pi = 170 and variance oſ = 1080. Construct an interval extending 2 standard deviations of 21 on each side of ui. <M1 < = 1430. Construct an interval (b) Suppose the second sample of 100 observations is selected from a population with mean M2 = 170 and variance o extending 2 standard deviations of C2 on each side of M2. < M2 < (c) Consider the difference between the two sample means (21 22). Compute the mean and the standard deviation of the sampling distribution of (71 - 72). mean = standard deviation = (d) Based on 100 observations, construct an interval extending 2 standard deviations of (71 - 22) on each side of (M1 - H2) < (11 - 12) <

Answer 1

Given dato: ni = 100 = 0,= 170 D2 = 100 % = 112=170 6,2 - 1080 02² - 1430 CI for 2 SD 95% CI -0.95 o = 1-0.95 = 0.05. -1.96 a) Zarz - 70-825 CI 95% = 3 + Z 412 x Jo 2 170 £ 1.96x 100 170 6.44 95%.5 = 163.56 <lls 176.44 6 95%CI 2 + 7x12? 2 = 170 £ 1.96 x 1430 100 170 t 7.41 95%CI = 162:59 < ll2 < 1774) c) Mean = (2-2) standard deviation ( 4 ) = -170-170 02 1080 + lu 30 100 -5.00999 nz 100 on 5.01 95% CI (2 t) t Id/2 * Tre + 1.96*5.01 ot 9.82 - 9.82 < l - lz & 9.82 95%CI 11