Question

7. You are given two random samples of paid claim amounts for two Hospitals, A and B. which independently follow normal distributions with equal variances and means A and MB. The results for the paid claim amounts are Hospital A: Hospital B: 6.21 7.34 5.67 7.88 7.89 10.12 9.71 5.55 3.89 4.33 12.48 The unbiased standard deviations calculated from the observations above are sa = 1.56 and so = 3.04. Let to be the critical value of a t random variable with v degrees of freedom. The following table lists values of ta., for specific combinations of a and v v=8 V=9 v = 10 a = 0.05 1.86 1.833 1.812 a = 0.025 2.306 2.262 2.228 Calculate the upper bound of the 95% confidence interval for the difference ub-HA

Answer 1

barn Hospital A 6.21 7.34 5.67 7.72 3.99 Hospitals "1.87 10-12 4.71 4.33 12.49 5.55 30.99 5o.uk ПА To = TB = 340 - 30.99 - 5198 [XB - 50.0e = 6-3 NB SB = 3.04 SA 21:56 variance pooled internal. for eto , we use confidence equel variance conduct the sp3 (n A-IISA²+ (A2-1) Sp2 # Pooled variance NA+MB-2 Sp² = (5-1) 1.562 +(5-1) 3:04? 5+6-2 - 6.2158 50²

# af anatno-2 a 5+6-2 va q xa significance level Tal-0.95 = 0.05. Critical ralece a = t.025 9 2.212 dz for ca the difference 95% 7 The upper bound د - مال (XB - TA) I tala ov spt - 22 621592 (+4) (8.347 -6-196) + 2.262 5.5639