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To evaluate the success of a 1-year experimental program designed to increase the mathematical achievement of underprivileged high school seniors, a random sample of participants in the program will be selected and their mathematics scores will be compared with the previous year's statewide average of 525 for underprivileged seniors. The researchers want to determine whether the experimental program has increased the mean achievement level over the previous year's statewide average. If alpha = .05, what sample size is needed to have a probability of Type II error of at most .025 if the actual mean is increased to 550? From previous results, s = 80. Suppose a random sample of 100 students is selected yielding y(bar) = 542 and s = 76. Is there sufficient evidence to conclude that the mean mathematics achievement level has been increased? Explain.

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