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, 8.90

B: 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 µA and µB be the respective population mean diameters across many similar hypothetical experiments. Consider a test at level α = 0.10 of H0 : µA − µB = 0 vs. HA : µA − µB 6= 0.(a) Do you think it is plausible that the samples came from approximately normal distributions? Why or why not?

Answer 1

(a) According to the central limit theorem, the distributions of the sample means of sufficiently large samples randomly selected from a population with mean, μ and standard deviation, σ with replacement will be normally distributed

Therefore, given that the size of the population from which the samples were selected (34 petri dishes) is comparable the sizes of the samples, (16 and 18), therefore, the samples are approximately normal

Also given that the petri dishes were prepared with growth medium designed to increase the growth of microorganisms, with an expected amount of growth, the samples therefore came from approximately normal distributions

Explanation: