Answer Happy

The following table shows the number of bacteria colonies
present in each of several petri dishes, after E. coli bacteria
were added to the dishes and they were incubated for 24 hours. The
"soap" dishes contained a solution prepared from ordinary soap; the
"control" dishes contained a solution of sterile water. The sample
means are 44 for the control group and 39.7 for the soap group;
thus the difference in sample means is 4.3, with the control being
larger, as would expected if the soap were effective. There are 20
possible randomizations of the six observations into two groups
each of size 3.
a. Create a list of these 20 randomizations (one of which is the
original assignment of observations to the two groups) and for each
case calculate the control mean minus the soap mean.
b. How many of the 20 randomizations produce a difference in
means at least as large as 4.3?
c. Is there evidence that the soap inhibits E. coli growth?
Justify your answer using the randomization results.