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SolutionHW2

# SolutionHW2 - Designed Experimentation Homework Answers for...

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Designed Experimentation Homework Answers for Assignment 2 Problem 3-6: a) Is there evidence to indicate the dosage level affects bioactivity? Use α =0.05. One-way ANOVA: Observation versus Dosage Source DF SS MS F P Dosage 2 450.7 225.3 7.04 0.014 Error 9 288.3 32.0 Total 11 738.9 S = 5.659 R-Sq = 60.99% R-Sq(adj) = 52.32% Answer: Yes, dosage level affects bioactivity, so we reject the null hypothesis that all dosage levels give equal responses. The significance level is at 98.6%. The dosage level explains 52% of the variability in bioactivity. b) If it is appropriate to do so, make comparisons between the pairs of means. What conclusions can you draw? Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev -------+---------+---------+---------+-- 20 4 29.750 5.439 (---------*--------) 30 4 36.750 5.439 (---------*--------) 40 4 44.750 6.076 (--------*--------) -------+---------+---------+---------+-- 28.0 35.0 42.0 49.0 Pooled StDev = 5.659 Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons among Levels of Dosage Individual confidence level = 97.91% Dosage = 20 subtracted from: Dosage Lower Center Upper ------+---------+---------+---------+--- 30 -4.177 7.000 18.177 (--------*--------) 40 3.823 15.000 26.177 (---------*--------) ------+---------+---------+---------+--- -12 0 12 24 Dosage = 30 subtracted from: Dosage Lower Center Upper ------+---------+---------+---------+--- 40 -3.177 8.000 19.177 (---------*--------) ------+---------+---------+---------+--- -12 0 12 24 Fisher 95% Individual Confidence Intervals All Pairwise Comparisons among Levels of Dosage Simultaneous confidence level = 88.66%

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Dosage = 20 subtracted from: Dosage Lower Center Upper ----+---------+---------+---------+----- 30 -2.053 7.000 16.053 (-------*------) 40 5.947 15.000 24.053 (-------*------) ----+---------+---------+---------+----- -12 0 12 24 Dosage = 30 subtracted from: Dosage Lower Center Upper ----+---------+---------+---------+----- 40 -1.053 8.000 17.053 (-------*------) ----+---------+---------+---------+----- -12 0 12 24 Answer: From the first plot of Individual 95% CI’s, it appears that there is a difference between the 20g and 40g dosage levels. The response seems to be linear, and there is not a significant difference between 20g and 30g, nor 30g and 40g. This suspicion is confirmed when examining the Tukey and Fisher test analyses. Tukey and Fisher both show that there is a sign change (i.e., zero is contained in the interval) for 20g and 30g, as well as for 30g and 40g.
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