Question

For the following problem: a. State the null and alternative hypotheses b. Determine the critical value of test statistic c. Compute the test statistic d. Make your decision e. State your conclusion 2. Cholesterol measurements from 24 vegetarians and 22 nonvegetarians yield the following data: Vegetarians: 115 125 170 170 200 215 125 170 225 130 175 230 130 175 130 175 140 180 150 180 155 180 165 185 Nonvegetarians: 105 110 115 170 170 175 240 245 125 180 125 185 130 200 145 215 160 220 165 230 165 240 Do vegetarians have lower cholesterol levels than nonvegetarians? Use a = 0.01

Answer 1

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Soln . Xx Vegeth corians Y Non Vegetarians a. Hypothesis testing. Let Mx - population means y Cholestrol measurement in vegetarians My population mean of cholestrol measurement in non vegetarian Null Hypothesis Ho: Mx = My lie means of cholested measurement of two groups (vegetarian and non vegetarian are same) acto against Hi: Mx. <My lievegtarians have lower cholestrol - (left tailed) level in than non vegetarians) Critical val t statistic t = locay) - Lux-HY N tnith-2(a) ni n2 ni= 24 m2 = 22. ĪC = 166:4583 y = 173.40911 tristn₂-2 (6) nitn2-2=24+22-2 = 46-2=44 i From t-table went dof d=0.01 Prob. (one-tailed) 180 40 un 2.423 44 x 60 1.2.390 Using Interpolation 40-44 -2.423.- 60 40 2.39.-2.423 - 4 - 2.423x = 2.423-X = 0.0066 20 -0.03 = x= 2.4164

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Critical region for the lefet tail test is t <- 2.4164 Critical value tyy(0.05) = 2.4164 (one tailed). Test statistics t = 5c-ý - CMx-My) unden Ho t = 5 - slitt - Jni nz nitn2-2 Sanna [26x -x)++ Ely-43"] - (2-x)+ + Ely-9)?) = [ 23273.96 + 41819.32] - 65093.28 = 1479.393 44 t = 166.4583 - 173.4091 1479-393/LUL (24 22 - 6.95076 = -0.61225 11-35 28 t calculated =-0.61225 7 -2.41.64 t calculated does not lie in critical region. Hence we really do not reject to.

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e conclusion lale do not reject at d=0.01 level of significance. Vegetarians have cholesterol level same as Non-Vegetarians because no significant difference in population. means of two opulation lie Vegetarians & Non-Vegetarians) found &