Question: A psychologist has prepared an "Optimism Test" that is administered yearly to graduating college seniors. The test measures how each graduating class feels about its future – the higher the score, the more optimistic the class. Last year’s class had a mean score of µ = 15. A sample of n = 9 seniors from this year’s class was selected and tested. The scores for these seniors are 7, 12, 11, 15, 7, 8, 15, 9, 6, which produce a sample mean M = 10 and SS = 94. On the basis of this sample, can the psychologist conclude that this year’s class has a different level of optimism than last year’s class? Note that this hypothesis test will use a t statistic because the population variance (σ ² ) is not known

1. State the hypotheses and determine the alpha level.
2. Locate the critical region.
3. Gather the data and compute the test statistic.
4. Make a decision about Ho and state the conclusion.
5. Calculate the effect size Cohen’s d and r ² .
6. Compute the power.

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