A sample is selected from a population with m 50 After a tr

A sample is selected from a population with m = 50. After a treatment is administered to the individuals in the sample, the mean is found to be M = 55 and the variance is s²= 64.
a. If the sample has n = 4 scores, then conduct a hypothesis test to evaluate the significance of the treatment effect and calculate Cohen

Solution

a) what value of X will make (42-40)/[10/sqrt(n)] = 1.96 (1.96 cuts off .025 in each tail of a standard normal variable.
0.2 sqrt(n) = 1.96; solve for n to get n=96.04 (take n=97)

b) (41-40)/[10/sqrt(n)] =1.96 ; 0.1 sqrt(n) =1.96; n=384.16 (take n=385)