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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-slow-wave sleep) and REM (rapid eye movement sleep). The data is available below. 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 specific 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 fit a Two-Way 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: Write down the mathematical model for this situation, defining all appropriate parameters State the appropriate hypotheses 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.

"HeartRates" "Shrews" "Sleep" 14 1 "LSWS" 12 1 "DSWS" 16 1 "REM" 26 2 "LSWS" 21 2 "DSWS" 22 2 "REM" 21 3 "LSWS" 20 3 "DSWS" 18 3 "REM" 19 4 "LSWS" 18 4 "DSWS" 17 4 "REM" 26 5 "LSWS" 23 5 "DSWS" 22 5 "REM" 20 6 "LSWS" 21 6 "DSWS" 19 6 "REM"