Please compute \"by hand calculations\" the ANOVA tables for each set of data, u

Question

Please compute "by hand calculations" the ANOVA tables for each set of data, using the summary statistics below. Present the 5 steps of the ANOVA hypothesis test. Please show all work.

Summary Statistics:

3. Four different concentrations of ethanol are compared at level a 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?

Explanation / Answer

null hypothesis: Ho: all mean are equal

alternate hypothesis: Ha: at least 2 mean are not equal

as p value 0.0000  is less then 0.05 level; ; and F stat, is high then F critical; hence we reject null hypothesis.

i ni Xi ni*(Xi-mean)^2 1 5 79.28 2857.245 2 5 61.54 190.036 3 5 47.92 277.885 4 5 32.76 2557.191 mean 55.375 5882.358 MSG Source of variation SS df MS F P value F crit Between groups 5882.358 3 1960.786 21.095 0.00001 3.238872 with in groups 1487.200 16 92.950 total 7369.558 19

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