Some soap manufacturers sell special antibacterial soaps. However, one might expect ordinary soap to also kill bacteria.

Question:

Some soap manufacturers sell special antibacterial soaps. However, one might expect ordinary soap to also kill bacteria. To investigate this, a researcher prepared a solution from ordinary, nonantibiotic soap and a control solution of sterile water. The two solutions were placed onto Petri dished and E. coli bacteria were added. The dishes were incubated for 24 hours and the number of bacteria colonies on each dish were counted. The data are given below. Compute the standard error of (Y1 - Y2) assuming (a) the two population variances are equal (b) the two population variances are not equal (c) Calculate a 95% confidence interval for the difference of two population means (Y1-Y2) using the result of part (b).