Question: In a northwestern university an SRS of 100 entering freshman in 2005 found that 20 finished in the bottom third of their high school class. Admission standards were tightened. In 2010 an SRS of 100 entering freshman found 10 finished in the bottom third of their high school class, Let p ₁ and p ₂ be proportion of freshman entering in 2005 and 2010 respectively who graduated in the bottom third of their high school class. Give a 99%, confidence interval for p ₁ – p ₂ ? Is there evidence that the population of freshmen in the bottom who graduated in the bottom third of their high school class in 2010 has been reduced, as a result of the tougher admission standards adopted in 2006 compared to the proportion in 2005? Implement a test for this claim. Follow the four steps procedure given in the text.

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