Exam 8: Inference for Proportions

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At a large Midwestern university,a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen finished in the bottom third of their high school class.Admission standards at the university were tightened in 1995.In 1997,a simple random sample of 100 entering freshmen found that only 10 finished in the bottom third of their high school class.Let p₁ and p₂ be the proportions of all entering freshmen in 1993 and 1997,respectively,who graduated in the bottom third of their high school class.Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school classes in 1997 was reduced as a result of the tougher admission standards adopted in 1995,compared to the proportion in 1993? To determine this,test the hypotheses H₀: p₁ = p₂ versus H_a: p₁ > p₂.What is the value of the z statistic for testing these hypotheses?