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, non-antibacterial soap and a control solution of sterile water. The two solutions were placed onto Petri dishes and E. coli bacteria were added. The dishes were incubated for 24 hours and the number of bacteria colonies on each dish was counted. The data are given in the following table.

Control Group X Soap Group Y 38 76 36 33 63 28 21 30 63 28 38 46 35 10 45 35 45 N 9 8 Sample mean 42.67 35.75 Sample SD 13.48 19.08 (a) Construct a 95% confidence interval for the difference between groups using the above data. Please interpret this confidence interval in the context of this study. A proper test should be performed to determine whether soap is more effective than the control. Conduct a two-sided hypothesis test at the 5% level. (b) Properly state both the null and alternative hypotheses in words and symbols. (c) Compute the test statistic. (d) Compute the P-value associated with your test statistics. (e) State the conclusion of the test in the context of this study. (f) Would you still reject your null hypothesis if the significant level was set at 10% (.1). Why or why not?

Answer 1

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