<\body> 1a. Use the data in the file factorial.txt. Compare the mean of growth when the coat is light to the mean when the coat is dark. Is the variance in the two cases significantly different? Are the distributions normal? 1b. Do a linear model of growth, that takes into account coat color. Is it significantly better than not taking coat color into account? Compare to the p-value you got in 1a. \; 2a. Draw 20 random points from a normal, and another 2 from a normal with mean 0.5. Does a t-test see them as significantly different? Does a Wilcoxon test see them as significantly different? 2b. Do the same as you did in 2a 1000 times with the t-test, and 1000 times with the Wilcoxon test. Are the success rates of the two tests significantly different from each other? try to find at what distance (i.e. mean of the second 20 samples) they become different. 3. Read the file strange.txt. Plot z vs. x. Do a linear regression of z vs. x. Does z increase or dercrease with x? Now do an analysis of variance of linear models for z. In the best model, does z increase or decrease with x? \; <\initial> <\collection> <\references> <\collection> |?>> <\auxiliary> <\collection> <\associate|toc> Excercise 3