Question

34 petri dishes are prepared with a growth medium. 16 are randomly selected and treated with antibiotic A. The other 18 are treated with antibiotic B. Each dish is inoculated with a bacteria. Several hours later,the diameter of the bacteria colony in each dish is measured in mm, with these results:A: 8.59, 7.80, 4.11, 8.68, 8.08, 7.86, 6.97, 8.21, 1.72, 8.13, 7.48, 6.33, 8.32, 8.65, 3.06, 8.90B: 5.59, 6.96, 5.25, 6.46, 0.09, 7.70, 3.10, 0.94, 7.00, 7.91, 6.39, 7.45, 5.79, 6.66, 5.91, 6.62, 5.07, 7.25 Let μAand μB be the respective population mean diameters across many similar hypothetical experiments.Consider a test at levelα= 0.10 ofH0:μA−μB= 0 vs.HA:μA−μB6= 0.

(a) Do you think it is plausible that the samples came from approximately normal distributions? Why or why not?

(b) Run a bootstrap test to evaluateH0using 5000 resamples.

(c) Use R to run a Wilcoxon Rank Sum test to evaluateH0.

Answer 1

1.(a)

so data is not normal