Three college students collected several pill-bugs from a woodpile and used them in an experiment in which they measured the time, in seconds, that it took for a bug to move 6 inches within an apparatus they had created. There were three groups of bugs: one group was exposed to strong light, for one group the stimulus was moisture, and a third group served as a control. The data are shown in the following table.41

Clearly the SDs show that the variability is not constant between groups, so a transformation is needed. Taking the natural logarithm of each observation results in the following dotplots and summary statistics.

For the transformed data, the ANOVA SS(between) is 53.1103 and the SS(within) is 23.5669.
(a) State the null hypothesis in symbols.
(b) Construct the ANOVA table and test the null hypothesis. Let α = 0.05.
(c) Calculate the pooled standard deviation, Spooled.

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86 20 ont-29 :24 26 3 3 4 4 28 4 6 9 5 6 8 3 5 4 20 7782 59 62 180 32 54 49 201 5 198 100 62 26 220 40-69 83 20 6909 102 2% 03 350 55 49 31 32 150 65 006 200 1-1 2 2 2 2 1 1 1 2 1.1 2 29 2 5 47 18 30 8 45 36 27 29 33 24 17 11 25 6 34 23 12 20 1 IS 5 그 Light Moisture Control Mean SD Light Moisture Control 2.99 0.65 4.98 0.62 4.99 0,66