Question: A researcher is investigating the effectiveness of a new study-skills training program for elementary school children. A sample of \(n=25.\) third-grade children is selected to participate in the program and each child is given a standardized achievement test at the end of the year. For the regular population of third-grade children, scores on the test form a normal distribution with a mean of \(\mu=150\) and a standard deviation of \(\sigma=25\). The mean for the sample is \(M=158\).

1. Identify the independent and the dependent variables for this study.
2. Assuming a two-tailed test, state the null hypothesis in a sentence that includes the independent variable and the dependent variable.
3. Using symbols, state the hypotheses \(\left(H_{0}\right.\) and \(\left.H_{1}\right)\) for the two-tailed test.
4. Sketch the appropriate distribution, and locate the critical region for \(\alpha=.05\).
5. Calculate the test statistic \((z\) -score) for the sample.
6. What decision should be made about the null hypothesis, and what decision should be made about the effect of the program?

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