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Part 3 of 4 - Written Answer #3 In an unpaired two-sample problem an experimenter observes a sample mean of 675 and a sample standard deviation of 44.76 in a sample of size 8 from population A and a sample mean of 702.4 and a sample standard deviation of 38.94 in a sample of size 17 from population B. (Enter your final answers only in the space provided and submit your work to obtain the answers on Gradescope.) 0.0 Points Question 1 of 3 Use the pooled variance procedure to construct a 99% two-sided confidence interval for PA-Hg.

Answer 1

# Letela be the mean of population A. eo be the mean of population B. given that For population A sample size, na 8 sample mean, 7A = 675 sample S.D. SA = 44.75 # for population ßi sample size, ng= 17 sample mean, TB = 702 sample S.DI SB = 38.94 a Here, we have to construct a gg.%. cent two-sided confidence internal for ela-elB. we know that a loo (1-2) % GI for el Arel B is, ((to -50); (8 - xo) i tale natha2 s 1 NA no where, pooled variance , s = nas + nos² S 8 (44.768 + 17 (38.942 8 +17-2 B = = 181706157 ..s= 426335 given that significance level (a)= "; t2/2, DATAB 2 = 0.01 (1.)) 2.8073 3

* Required at is, (cops - 902) 7 218673 x 42.6335 8 -78.3152, 24.3152 Here we have to construct a 99% two-sided o. L. for MA-ulo assuming unequal population variance (ie o'n #ca) "A required at - is. (C&A - Pe) ; (XA - *B) 7 tala, na +0g-2 .s. 1 NA + no where 2 $ ("All S + (no-1) sa HAINB-2 .; = 1444.40)2 + (10) (38.9402 9717 -2 - 2 $= 1664, 5818 .:S= 400 7993 G is, (1699-702) + I 2.8073 x 40.1993 17. (-70.1875e 22.1095) for the both ol 1) and 2) confidence interval does not contain - go. therefore we reject the null hypothesis at 1% level of significance (test, Hoi lla-elB= -80.rs ela elg & -80