LINK TO DATA
https://drive.google.com/open?id=0Bwos1D7Lt802TEVVZzJLSV9lRmtWZ1VmV1lickdsSDVTdFk0
Exercises3 and 6,p. 359.On part (c) of each problem, you do not have to do the tests of equal variances.However, you should do the rest of what is askedof you in (c).Use the function shapiro.test in R to test normality of the residuals.To obtain residuals, if you have put the output of aovin an R object called fit, then fit$residwill give you the residuals.
3.. Four different concentrations of ethanol are compared at level or = 0.05 for their effect on sleep time. Each concentration was given to a sample of 5 rats and the REM (rapid eye movement) sleep time for each rat was recorded (SleepRem.trt). Do the four concentrations differ in terms of their effect on REM sleep time? (a) State the relevant null and alternative hypotheses for answering this question, and use hand calculations to conduct the ANOVA F test at level of signicance 0.05. State an},r assumptions needed for the validity of this test procedure. (Hint. You may use the sum mary statistics f1 = T928, f2 = 61.54, 33 : 4192, T4 = 32.16, and MSE = 3% = 92.95.) (13} Import the data into the R data frame 3!, and use the R command enovcfcovfslvaiu eswsftn {ii} to conduct the ANOVA F test. Give the ANOVA table, stating the pwvalue, and the outcome of the test at level of significance 0.05. (c) Use R commands to test the assumptions of equal variances and normality. Report the p-values from the two tests and the conclusions reached. Next, construct a boxplot and the normal Q-Q plot for the resid- uals, and comment on the validity of the normality assumption on the basis of these plots. 6. Porous carbon materials are used commercially in several industrial applications, including gas separation, membrane separation, and fuel cell applications. For the purpose of gas separation, the pore size is imporv tant. To compare the mean pore size of carbon made at temperatures (in C'C) of 300, 400, 500, and 600, an experiment uses 5 measurements at each temperature setting (PorousCorborert). Is there any dierence in the average pore size of carbon made at the different temperatures\"? (a) State the relevant null and alternative hypotheses for answering this question, and use hand calculations to conduct the ANOVA F test at level or = 0.05, statv irrg any assumptions needed for its validity. (Hint. You may use the following summary statistics: f1 = 143, f2 = 124, f3 = 6.66, f4 = 6.24, 3% = 0.2245, 3% = 0.143, 3% = 0.083, SE = 0.068.) (b) Use R commands to import the data into the R data frame pr: and to conduct the ANOVA F test. Report the value of the test statistic, the pvalue, and whether or not the null hypothesis is rejected at level or : 0.05. (c) Use R commands to test the assumptions of equal variances and normality. Report the p-values from the two tests and the conclusions reached. Next, construct a borrplot and the normal Q-Q plot for the residuals from tting the model (10.2.2), and comment on the validity of the normality assumption on the basis of these plots
