N1. {Two-Sample Mean Test when 111 at 22] As an extension to Wednesday's discussion, what if the two samples have different variance structures. In a large sample problem, we can do the same procedure but with an approximate x2 test. A condence ellipsoid for #1 x is all 111 p2 satisfying _ 1 1 1 _ iX2_(F1_ #2)];(17 31 1+7: 32) iX2_(F1_P2)]ng(a) 2 Suppose two measurements of power usage for electric car drivers (11.1 = 56) and non-electric car drivers (:12 = 89).'I'he summary statistics are: = [2044 s 33.3 23 5555 1: 238 731 [1303] s _ 5.3 195] L2 355 195 550 Find 95% simultaneous condence intervals for the differences in the mean components and discuss what can be concluded in this test. Answer: Under Null Hypothesis, EH #1 = #2 i.e.,1t1- #2 =0 Vs H1 ' P1 9'5 #2 The test statistic is: Equation]: 2 1 1 '1 _ _ T =[X1X2(P1P-2H 51+52 [X1X2(P1P2N n1 n2 5 2%) Where 111 = 56,112 = 89 \fWe reject Ho if, 1X1 - X21' ( S1 + 7 52) 181 -821> X3(a) As x(a) (from table of x2) for p=2 at a = 0.05 => 5.991 Conclusion: Since, T2 > xp(a) , So we reject out null hypothesis at 5% level of significance. 95% confidence interval for the difference in the mean component: 2 S2k (X1k - X2k) + Xpa S1k + n1 n2 For 1st Variable: 2- (X11 - X21) + 5.991 $11 + $21" n1 n2 138.32 86.32 > (2044 -1300) + 5.991 + 56 89 (744) + 5.991 [341.55 + 83.68] (744) + V5.991 [425.23] (744) + V2547.55 (744) + 50.473\fE1. (6.1) Consider the ethical statistics guidelines laid out by the American Statistical Association. Statistical errors can be technical and sometimes even buried within conventional practices such as taking a statistically signicant comparison as strong evidence in favor of a favored hypothesis. How would you report the result of N1 when the results were not in your favor? Analyze your ethical decision made from the Christian worldview