Question 2 [25 marks] A research team monitored the heart rates for six randomly selected tree shrews (Tupaia glis) during three different stages of sleep: LSWS (light slow-wave sleep); DSWS (deep-slowwave sleep) and REM (rapid eye movement sleep). The data is available in the le TreeShrews . dat on iLearn. The authors wish to account for any differences between the tree shrews and stages of sleep. HeartRates The heart rates of the tree shrew Shrews The specic tree shrews (labelled as 1, 2, 3, 4, 5 and 6) Sleep The stages of sleep (labelled as \"LSWS,\" \"DSWS,\" \"REM\") a. [2 marks] For this study, is the design balanced or unbalanced? Explain why. b. [5 marks] Construct two different preliminary graphs that investigate different features of the data and comment. c. [2 marks] Explain why we cannot t a TwoWay ANOVA with interaction model to this dataset. d. [12 marks] Analyse the data, stating the null and alternative hypothesis for each test, and check assumptions. In your answer: 0 Write down the mathematical model for this situation, dening all appropriate parameters 0 State the appropriate hypotheses 0 Compute an appropriate ANOVA table . Check assumptions e. [4 marks] State your conclusions about the effect of Shrews and Sleep on HeartRates. These conclusions are only required to be at the qualitative level and can be based off the outcomes of the hypothesis tests in c. and the preliminary plots in b. You do not need to statistically examine the multiple comparisons. > tree = read . table("TreeShrews . dat", header = TRUE) > tree HeartRates Shrews Sleep 14 1 LSWS 12 1 DSWS 16 1 REM 26 2 LSWS 6 0 NOVIA WNY 21 2 DSWS 22 2 REM 21 LSWS 20 DSWS . W W W 18 REM 10 19 4 LSWS 11 18 4 DSWS 12 17 4 REM 13 26 5 LSWS 14 23 5 DSWS 15 22 5 REM 16 20 6 LSWS 17 21 6 DSWS 18 19 6 REM