Question

1. A manufacturer of heart pacemakers is investigating changing the casing material to decrease the weight of the device. Three different alloys are being considered Eight prototype parts are made from each alloy material and weighed (in g). The data are compiled into the following (partially complete) ANOVA table: Source of Variation Sum of Squares 4.1408 Degrees of Freedom Mean Squares Fo Treatment Error Total 21 4.8596 (a) Complete the ANOVA table. (b) Use the ANOVA table to test the hypothesis that changing the casing material decrease the weight of the device and draw the appropriate conclusions. Use α-0.01. (To gain full credit, you should provide the following i. State the hypotheses. ii. Test statistic. iii. What is the distribution of the test statistic? iv. Decision (Show all your work v. Conclusion in the context of the problem.

Answer 1

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a) ANOVA Table Source of variation Sum of squres Degrees of freedom Mean square Factor ror Total C- atm entsMS, Treatm erts Treaent MSg MS an-1 Completed ANOVA Table Source of vari ati on Sum of squares Degrees of freedomMean square 408=2.0704 | 2070426048747 a-1 3-1 2 Factor 4.1408 0.7188 3810.7188-0.0342 - 21 60.487479130.0000 0.0342 ror 21 4.8596 an-1 3(8)-123 Total b) To test H0 : β=0 versus The level of significance is α = 0.10 The test statistic is given by MST MSE 2.0704 0.0342 60.48747913 The P-value=0.000€ α = 0.10 Hence we reject Ho Conclusi on Hence we conclude that the weight differs among the alloy types