Question

Chapter 6, Section 4-CI, Exercise 190 Use the t-distribution to find a confidence interval for a difference in means un – U2 given the relevant sample results. Give the best estimate for uy - U2, the margin of error, and the confidence interval. Assume the results come from random samples from populations that are approximately normally distributed. A 99% confidence interval for ulj - uz using the sample results īj = 547, si = 127, ni = 400 and 12 = 459, 32 = 95, n2 = 200 Enter the exact answer for the best estimate and round your answers for the margin of error and the confidence interval to two decimal places. Best estimate = Margin of error = Confidence interval :

Answer 1

solotion:- Fsom the given data = 547 459 S, = 127 S2 - 95 400 n2 = 200 *. Now we find Best estimate (u-l2) = - 547-459 MrMz = 88 *. We find Margin of e M.E = teh,de) (12-1). (15)* ctro01/2 dif) 400 200 t0.005,df)40.3225+ 45.125 %3D df

(27) (95)* 400 200 400 200 400-1 200-1 (40.3225+45.125) (40.3215) (45125)* 399 199 7301.275 4.0749+ 10. 2324 7301.275 14.3073 d.f = 510.318 4h, dt) = 2. 5855 2.5855 40.3225+45.125 Margin of erros = = 2.5855 J85.4475 = 2.5855 (9.24378) = 23.8997 M.E = 2 3.89 we find *. Now confidence intexyal CI = (7-7)+ ME

(3) From the above we have C.I = 88¢ 23.89 -(88+23.89 , 88 - 23.89 = (111.89, 64.11) to 64.11 confidence interval = lll.89