Question: A researcher is evaluating the effectiveness of a new physical education program for elementary school children. The program is 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 \(\mu=40\) and \(\sigma=8\)

1. 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 \(\alpha=.05\).
2. If the sample mean is \(M=44\), is this enough to demonstrate a significant effect? Again, assume a two-tailed test with \(\alpha=.05\).
3. Briefly explain why you reach different conclusions for part (a) and part (b).

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