3. Four different concentrations of ethanol are compared at level = 0.05 for their effect on sleep time. Each concentration was given to a

3. Four different concentrations of ethanol are compared at level α = 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.txt). 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 significance 0.05. State any assumptions needed for the validity of this test procedure. (Hint. You may use the summary statistics X1 = 79.28, X2 = 61.54, X3 = 47.92, X4 = 32.76, and MSE = S2 p = 92.95.)

(b) Import the data into the R data frame sl, and use the R command anova(aov(sl$values∼sl$ind)) to conduct the ANOVA F test. Give the ANOVA table, stating the p-value, 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 residuals, and comment on the validity of the normality assumption on the basis of these plots.