Question

1. Consider the hypothesis test Ho: M1= H2 against Hj: Mit u2. Suppose that sample sizes are ni = 13, N2 = 10 ži=4.7, X2 =6.8, S1=2 and s2 =2.5. Assume that the data are randomly drawn from two independent Normal distributions (a) Confirm that it is reasonable to assume o = ož by completing the steps i. through v. below. Use a = 0.05. Ho: 01 = ož Họ: 0 + 03 i. Test Statistic: ii. Rejection Criterion: iii. Decision (reject or do not reject the null hypothesis): iv. The probability you made an incorrect decision: v. Conclusion (state in the terms of this test):

Answer 1

given 4 = 4.7 213, 12:10 30.05 Ho: 612 6st vs Hi8 2² 22 f statistics critical Emine) Fas ~ F(n,r, ner] = = F( 12,9) F(1-4/2) = (292 (2.592 -0.64 Flaccutated) > F 99.9(xx) = 612,9 (0.025) - 3.87 F< F1918(1-4X) = F12,9 (1-x) = F12.9(0.975) = 2-2906 Accepted fls, glosy fealas a fira, 10.025) osuerwise rejected (1) F (0.975) c cam c Flows) 12,9 8.99 < 0.64 < 3.87 Aleeft

(iv) P = PC Fcat > 0.64) -0.23 (By table) PC.F?1:563.) -0.755 P = ( Fu > 3 ) (V) conclusion : caleculated value of Fio between the tabulated value, hence neue Hypothesis accepted at 5.1. =4 level of significance

Appendix V (Continued) F.025, ... Degrees of freedom for the numerator (0) 1 2 3 4 5 6478 799 3 864.2 899.6 921.8 937.1948.2 956,7 38.51 39.00 39.17 39.25 39.30 39.33 39.36 111.44 1845 or 699.30 9.07 1001 843 7.76 7.39 715 6.98 6.85 8.81 7.26 6.60 6.23 5.99 Degrees of freedom for the denominator (1) 1 ten ما با 1.98 192 मननस SSR 2.07 1.94 416 0 2.14 2012 201 1 04 1.88 1.82 1.69 1.88 1.74 1.80 1.7 1.67 13 APPEN

Appendix II (Continued) Le du 0(2)=L-77 Appendix 11 Cumulative Standard Normal Distribution (2)= 2 SC 0.61026 0 1 0.01 0.00 0.02 0.03 0.04 t 0.50000 OD 0.50399 0.50798 0.31595 0.0 051197 0.1 0.5398) 0.1 0.54379 0.55561 0.55172 0.54776 02 0.57926 0.58317 0.58706 0.59095 0.59483 0.2 0.61791 0.3 0.62172 0.62920 0.62551 0.63307 0.3 0.65342 0.4 0.65910 0.62276 0.67003 0.4 0.66640 05 0.69146 0.69497 0.69847 0.70194 0.70540 0.3 0.6 0.71575 0.72907 0.73237 0.73565 0.73891 0.6 0.7 0.75803 0.76115 0.76424 0.76730 0.77035 0.7 0.1 076314 0.79103 0.79389 0.79673 0.79954 0.8 09 0.81594 0.81859 0.82121 0.82381 0.82639 0.9 10 0.84134 0.84375 0.84613 0.84849 0.850R3 1.0 1.1 0.86433 0.86650 0.86864 0.87070 0.87285 1.1 12 0.88493 0.88686 0.88877 0.89065 0.89251 1.2 13 0.90320 0.90490 0.90658 0.90824 0.90988 1.3 14 0.91924 0.92073 0.92219 0.92364 0.92506 1.4 1.5 0.93319 0.93448 0.93574 0.93699 0.93822 1.5 16 0.94520 0.94630 0.94738 0.94845 0.94950 1.6 1.7 0.95543 0.95637 0.95728 0.95816 0.95907 1.7 1.8 0.96407 0.96485 0.96562 0.96637 0.96711 1.8 1.9 0.97128 0.97193 0.97257 0.97320 0.97381 1.9 20 0975 0.97778 0.97831 0.97882 0.97932 2.0 2.1 0.98214 0.98257 0.98300 0.98341 0.98382 2.1 2.2 0.98610 0.98645 0.98679 0.98713 0.98745 22 23 0.98928 0.98956 0.92983 D:99010 0.99036 23 2.4 0.99180 0.99202 0.99224 0.99245 0.99266 2.4 2.5 0.99379 0.99396 0.99413 0.99430 0.99446 25 2.6 0.99534 0.99547 0.99560 0.99573 0.99585 26 27 0.99653 0.99664 0.99674 0.99683 0.99693 2.7 28 0.99744 0.99752 0.99760 0.99767 0.99774 2.8 29 0.99813 0.99819 0.99825 0.99831 0.99836 2.9 3.0 0.99865 0.99869 0.99874 0.99878 0.99882 3.0 3.1 0.99903 0.99906 0.99910 0.99913 0.99916 3.1 32 0.99931 0.99934 0.99936 0.99938 0.99940 3.2 3.3 0.99952 0.99953 0.99955 0.99957 0.99958 3.4 0.99966 0.99968 0.99969 0.99970 0.99971 3.4 3.5 0.99977 0.99978 0.99978 0.99979 0.99980 3.5 3.6 0.99984 0.99985 0.99985 0.99916 0.99986 0.99986 3.6 3.7 0.99989 0.99900 0.99990 0.99990 0.99991 3.7 3.8 0.99993 0.99993 0.99993 0.99994 0.99994 3.8 3.91 0.99995 0.99995 0.99996 0.99996 0.99996 3.9 0.05 0.0 0.51994 0.1 0.55962 0.2 0.59871 03 0.63683 04 0.67364 0.5 0.70884 0.6 0.74215 0.7 0.77337 0.8 0.80234 0.9 0.82894 10 0.85314 1.1 0.17493 1.2 0.89435 1.3 0.91149 1.4 0.92642 1.5 0.93943 1.6 0.95053 1.7 095994 1.8 0.96784 1.9 0.97441 2.0 0.97982 2.1 0.98422 2.2 0.98778 23 0.99061 2.4 0.99286 25 0.99461 2.6 0.99598 2.7 0.99702 28 0.99781 2.9 0.99841 3.0 0.99886 3.1 0.99918 3.2 0.99942 33. 0.99960 34 0.99972 35 0.99981 3.6 0.99987 3.7 0.99991 3.8 0.99994 3.9 0.99996 ODS 0.52392 0.56356 0.60257 064058 067724 0.71226 0.74537 0.77637 0.80510 0.83147 0.85543 0.87697 0.89616 0.91308 0.92785 0.94062 0.95154 0.96080 0.96856 0.97500 0.98030 0.98461 0.98809 0.99086 0.99305 0.99477 0.99609 0.99711 0.99788 0.99846 0.99889 0.99921 0.99944 0.99961 0.99973 0.99981 0.99987 0.99992 0.99994 0.99996 0.07 0.52790 0.56749 0.50542 0.64431 0.68082 0.71566 0.7467 0.77935 0.80785 0.83397 0.85769 0.87900 0.89796 0.91465 092922 0.94179 0.95254 0.96164 0.96926 0.97558 0.98077 0.98500 0.98840 0.99111 0.99324 0.99492 0.99621 0.99720 0.99795 0.99851 0.99893 0.99924 0.99946 0.99962 0.99974 0.99982 0.99988 0.99992 0.99995 0.99996 0.08 OD9 { 0.53188 053586 00 0.57142 0.57534 0.1 0.61409 0.2 0 64803 0.65173 03 0.68438 0.68793 04 0.71904 Q.72240 0.5 0.75175 a 75490 0.6 0.78230 10.78523 2.7 0.81057 0.81327 0.8 0.83646 0.83891 09 0.85993 0.86214 10 0.88100 0.88297 1.1 0.89973 090147 1.2 0.91621 091773 1.3 0.93056 0.93189 1.4 0.94295 0.94408 15 0.95352 0.95448 1.6 0.96246 0.96327 1.7 0.96995 0.97062 1.8 0.97615 0.97670 1.9 0.98124 0.98169 20 0.98537 0.98574 2.1 0.98870 0.98899 2.2 0.99134 0.99158 23 0.99343 0.99361 2.4 0.99506 0.99520 2.5 0.99632 099643 2.6 0.99728 0.99736 2.7 0.99801 0 99807 2.8 0.99856 0.99861 2.9 0.99897 0.99900 3.0 0.99926 0.99929 3.1 0.99948 0.99950 3.2 0.99964 0.99965 3.3 0.99975 0.99976 3.4 0.99983 0.99983 33 0.99988 0.99989 3.6 0.99992 0.99992 3.7 0.99995 0.99995 38 0.99997 0.99997 3.9