10. A physician who specializes in weight control has three different diets she recommends.As an experiment, she randomly selected 15 patients and then assigned 5 to each diet. Afterthree weeks the following weight losses, in pounds, were noted. At the 0.05 significancelevel, can she conclude that there is a difference in the mean amount of weight loss amongthe three diets?|Plan APlan BPlan C56777479|558469ANOVA Table for the above data is as follows:SourceSum of Squares dfMean Square F(computed) F(critical)Treatment?????Error??0.967Total37.73?Using the 0.05 significance level: (a) state the null and alternate hypotheses for treatment;(b) state the decision rule for treatments; (c) complete and ANOVA table above (put thevalue next to the question mark); (e) give your decision regarding the hypothesis.

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Description: 10. A physician who specializes in weight control has three different diets she recommends.As an experiment, she randomly selected 15 patients and then assigned 5 to each diet. Afterthree weeks the following weight losses, in pounds, were noted. At

Consider the model:- yij=μ+αi+eij, where eij~N(0,σ2),for all i=1,2,3, and j=1,2,..,5Here, i=1 represents A, 2 represents B and 3 represents C.Also, μ: General effect and αi: Additional effect due to treatment i. Here, the testing of hypothesis is: H0:αi=0, for all i=1,2,3 vs H1: Not H0 The estimates of model parameters are: μ^=115∑i=13∑j=15yij=y00 and αi^=15∑j=15yij=yi0 Thus, the Sum of Square estimates will be SSE=∑i=13∑j=15(yij-yi0)2 SSTr=∑i=135(yi0-y00)2SST∑i=13∑j=15(yij-y00)2=SSTr+SSEAlso, the degrees of freedom will bedfSStr=2dfSSE=12dfSST=14Thus,MSTr=SSTrdfSStr,MSE=SSEdfSSEIf, F=MSTrMSE,then, F~F2,12.Hence, we reject H0 if F(computed)>F(critical)=F0.05;2,12=3.885Then, consider the given table: Treatment ∑j=15yij yi0 (yi0-y00)2 Plan A 25 5 2.1609 Plan B 31 6.2 0.0729 Plan C 41 8.2 2.9929 Also, y00=9715=6.47 Hence, SSTr=5×(2.1609+0.0729+2.9929)=5×5.2267=26.1335SSE=SST-SSTr=37.73-26.1335=11.5965 Hence, the ANOVA table will be: Source Sum of Squares DF Mean Squares F(computed) F(critical) Treatment 26.1335 2 13.06675 13.5214 3.885 Error 11.5965 12 0.966375 Total 37.73 14 Thus, we reject the null hypothesis and conclude that there is difference in the mean amount of weight loss.

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10. A physician who specializes in weight control has three different diets she recommends. As an experiment, she randomly selected 15 patients and then assigned 5 to each diet. After three weeks the following weight losses, in pounds, were noted. At the 0.05 significance level, can she conclude that there is a difference in the mean amount of weight loss among the three diets? | Plan A Plan B Plan C 5 7 7 7 8 4 7 9 8 9 4 ANOVA Table for the above data is as follows: Sum of Squares df ? Mean Square F(computed) F(critical) Source Treatment ? ? ? Error ? ? 0.967 Total 37.73 ? Using the 0.05 significance level: (a) state the null and alternate hypotheses for treatment; (b) state the decision rule for treatments; (c) complete and ANOVA table above (put the value next to the question mark); (e) give your decision regarding the hypothesis.

10. A physician who specializes in weight control has three different diets she recommends. As an experiment, she randomly selected 15 patients and then assigned 5 to each diet. After three weeks the following weight losses, in pounds, were noted. At the 0.05 significance level, can she conclude that there is a difference in the mean amount of weight loss among the three diets? | Plan A Plan B Plan C 5 7 7 7 8 4 7 9 8 9 4 ANOVA Table for the above data is as follows: Sum of Squares df ? Mean Square F(computed) F(critical) Source Treatment ? ? ? Error ? ? 0.967 Total 37.73 ? Using the 0.05 significance level: (a) state the null and alternate hypotheses for treatment; (b) state the decision rule for treatments; (c) complete and ANOVA table above (put the value next to the question mark); (e) give your decision regarding the hypothesis.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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