Part 1: 2-Factor ANOVA - Analysis of Raw DataPart 2: 2-Factor ANOVA based on Summary StatisticsSTA 6166 – Fall 2006Projects 4&5Part 1: 2-Factor ANOVA - Analysis of Raw DataA study of the effect of 4 temperature settings on percent shrinkage in dyeing fabrics was made on on 4 replications for each of 3 types of fabric in a completely randomized design. The data are the percent shrinkage of three replicate fabric pieces dried at each of the 4 temperatures, and are in file: shrink.dat. Write out the linear model, and obtain the analysis of variance for the data. Plot the means by temperature with separate “profiles” for each fabric. See project 1. Test whether there is a fabric x temperature interaction at the =0.05 significance level. Clearly state: null and alternative hypotheses, test statistic, rejection region and P-value. Include any computer output you obtain. Test for a temperature main effect at the =0.05 significance level. Clearly state: null and alternative hypotheses, test statistic, rejection region and P-value. Include any computer output you obtain. Test for a fabric main effect at the =0.05 significance level. Clearly state: null and alternative hypotheses, test statistic, rejection region and P-value. Include any computer output you obtain. Conduct any post-hoc comparisons you feel are appropriate based on your analysis. (Experimentwise =0.05) Write a brief, but thorough, description of your results.Part 2: 2-Factor ANOVA based on Summary StatisticsExperiments were conducted in mice receiving various doses of recombinantbovine growth hormone (rbGH). Samples of 30 male and 30 female Charles River CD rats were obtained and randomized (presumably) so that five males and 5 females received each of the following 6 treatments: Control (No rbGH) Subcutaneous Injection of 1.0 mg/kg per day Oral Gavage of 0.1 mg/kg per day Oral Gavage of 0.5 mg/kg per day Oral Gavage of 5 mg/kg per day Oral Gavage of 50 mg/kg per dayOne primary response measured was body weight gain (grams) at study day 85. The means and standard deviations are given in the following table.Treatment Male Mean (SD) Female Mean (SD)Control 324 (39.2) 148 (24.4)Subcut Inj 1.0 432 (60.3) 217 (32.3)Oral 0.1 327 (39.1) 140 (19.6)Oral 0.5 318 (53.0) 152 (31.0)Oral 5 325 (46.3) 147 (22.0)Oral 50 328 (43.0) 152 (20.5) Obtain the Analysis of Variance for this dataset. Test whether there is a Treatment x Gender interaction (=0.05) Test for Treatment main effects (=0.05) Test for Gender main effect (=0.05) For these 12 conditions, plot the standard deviations versus the means. Do you see a particular pattern? Write a brief, but thorough, description of your results.Part 3: Chi-Square Test for AssociationA study was conducted, investigating the prevalence of Baylisascaris procyonis eggs in Procyon lotor fecal samples during 4 seasons of the year. The following contingency table classifies sampled Procyon lotor fecal samples by season and presence/absence of of Baylisascaris procyonis eggs.Season Fecal Samples with eggs Fecal Samples w/out eggsJuly-August 5 46September-November 45 61December-February 2 22March-May 4 92 Obtain a table of expected cell counts, under the hypothesis that the prevalence of the eggs in fecal samples is independent of season. Conduct the Pearson chi-square test to determine whether the prevalence of the eggs in fecal samples is independent of season (=0.05). Obtain a cluster bar graph of egg presence/absence in fecal samples, separately by
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