A random sample of n = 12 individuals is selected from a population with m = 70, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M =...

A random sample of n = 12 individuals is selected from a population with m = 70, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 74.5 with SS = 297.

a. How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.)

b. If there is no treatment effect, how much difference is expected just by chance between the sample mean and its population mean? That is, find the standard error for M. (Note: In a hypothesis test, this value is the denominator of the t statistic.)

c. Based on the sample data, does the treatment have a significant effect? Use a two-tailed test with a = .05.