Question: A researcher is evaluating the effectiveness of a new physical education program for elementary school children. The program for designed to reduce competition and increase individual self-esteem. A sample of n= 16 children is selected and the children are placed in the new program. After 3 months, each child is given a standardized self-esteem test. For the general population of elementary school children, the scores on the self-esteem test form a normal distribution with µ=40 and ?=8.

a. If the researcher obtains a sample mean of M= 42, is this enough evidence to conclude that the program has a significant effect? Assume a two-tailed test with α= .05.

b. If the sample mean is M= 44, is this enough to demonstrate a significant effect? Again,

assume a two-tailed test with α= .05.

c. Briefly explain why you reached different conclusions for part a and b.