\fnew table 5 A Q Search +) v APPENDIX B B ABLE 5 Critical Values of the x2 Distribution A x2 Degrees of X'-025 X-010 X-005 Freedom X-995 X-990 X-975 X-950 X-900 X-100 X:050 0.0158 2.71 3.84 5.02 6.63 7.88 0.000039 0.000157 0.000982 0.00393 0.0201 0.0506 0.103 0.211 4.61 5.99 7.38 9.21 10.6 0.0100 0.352 0.584 6.25 7.81 9.35 11.3 12.8 0.072 0.115 0.216 7.78 9.49 11.1 13.3 14.9 0.207 0.29 0.484 0.711 1.06 12.8 15.1 16.7 0.412 0.554 0.831 1.15 1.61 9.24 11.1 12.6 14.4 16.8 18.5 0.676 0.872 1.24 1.64 2.20 10.6 1.69 2.17 2.83 12.0 14.1 16.0 18.5 20.3 0.989 1.24 20.1 22.0 1.34 1.65 2.18 2.73 3.49 13.4 15.5 17.5 2.09 2.70 3.33 4.17 14.7 16.9 19.C- 21.7 23.6 1.73 16.0 18.3 20.5 23.2 25.2 2.16 2.56 3.25 3.94 4.87 5.58 17.3 19.7 21.9 24.7 26.8 2.60 3.05 3.82 4.57 18.5 21.0 23.3 26.2 28.3 6.30 12 3.07 3.57 4.40 5.23 5.01 5.89 7.04 19.8 22.4 24.7 27.7 29.8 13 3.57 4.11 21.1 23.7 26.1 29.1 31.3 14 4.07 4.66 5.63 6.57 7.79 32.8 15 4.60 5.23 6.26 7.26 8.55 22.3 25.0 27.5 30.6 6.91 7.96 9.31 23.5 26.3 28.8 32.0 34.3 16 5.14 5.81 35.7 5.70 6.41 7.56 8.67 10.1 24.8 27.6 30.2 33.4 34.8 37.2 6.26 7.01 8.23 9.39 10.9 26.0 28.9 31.5 10.1 11.7 27.2 30.1 32.9 36.2 38.6 6.84 7.63 8.91 10.9 12.4 28.4 31.4 34.2 37.6 40.0 20 7.43 8.26 9.59 41.4 8.03 8.90 10.3 11.6 13.2 29.6 32.7 35.5 38.9 11.0 12.3 14.0 30.8 33.9 36.8 40.3 42.8 8.64 9.54 38.1 41.6 44.2 23 9.26 10.2 11.7 13.1 14.8 32.0 35.2 15,7 33.2 36.4 39.4 43.0 45.6 24 9.89 10.9 12.4 13.8 37.7 40.6 44.3 46.9 25 10.5 11.5 13.1 14.6 16.5 34.4 13.8 15.4 17.3 35.6 38.9 41.9 45.6 48.3 26 11.2 12.2 27 12.9 16.2 18.1 36.7 40.1 43.2 47.0 49.6 11.8 14.6 48.3 51.0 28 12.5 13.6 15.3 16.9 18.9 37.9. 41.3 44.5 16.0 17.7 19.8 39.1 42.6 45.7 49.6 52.3 13.1 14.3 15.0 18.5 20.6 40.3 43.8 47.0 50.9 53.7 13.8 16.8 29.1 51.8 55.8 59.3 63.7 66.8 20.7 22.2 24.4 26.5 $4.8 63.2 67.5 71.4 76.2 79.5 28.0 29.7 32.4 37.7 92.0 35.5 37.5 40.5 43.2 46.5 74.4 79.1 83.3 88.4 8883868 95.0 100 104 43.3 45.4 48.8 51.7 55.3 85.5 90.5 51.2 53.5 60.4 64.3 96.6 102 107 112 116 57.2 124 128 59.2 61.8 65.6 69.1 73.3 108 113 118 136 67.3 130 140 70.1 74.2 77.9 82.4 118 124Instruct ions 0 For hypothesis testing problems, please indicate critical value (or values), state rejection rule, evaluate test statistic, and nally, formulate your decision in the form YES, enough evidence to reject the null hypothesis or NO, not enough evidence to reject H0. 0 For condence intervals, specify critical values and indicate the formula that you are using for limits, UCL and LCL 0 You Will need critical values for t and x2-distributions (Tables 4 and 5 in the textbook). Problem 2 [10 points = 5 + 5] Actuaries also intend to compare the average stock value for two companies. They assume that the stock prices are normally distributed. Two samples of size n = 8 were selected independently and their summaries were derived as follows. Actuaries believe that two population variances are entirely unknown. Company Size Mean = X Variance = S2 v = $2 High Tech n1 = 8 (X)1 = 70.3 (S1) 2 = 28 V1 = 3.5 Retail n2 = 8 (X ) 2 = 80.9 (S2)2 = 100 V2 = 12.5 1. At the significance level, a = 0.01, do actuaries have evidence that average high tech stock is below than retail? 2. Estimate the average difference High Tech - Retail with confidence = C = 0.95 Solution