In a large midwestern university (the class of entering freshmen being on the or

Question

In a large midwestern university (the class of entering freshmen being on the order of 6000 or more students), an SRS of 100 entering freshmen in 1993 found that 20 finished in the bottom third of their high school class.  Admission standards at the university were tightened in 1995.  In 1997 an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class.  Let p1 and p2 be the proportion of all entering freshmen in 1993 and 1997, respectively, who graduated in the bottom third of their high school class.  What is the 90% confidence interval for p1 - p2?

-0.10

-0.10

Explanation / Answer

p1=20/100=0.2

p2=10/100=0.1

Given a=0.1, Z(0.05)=1.645 (from standard normal table)

So 90% confidece interval is

(p1-p2)+/-Z*sqrt(p1*(1-p1)/n1 +p2*(1-p2)/n2)

--> (0.2-0.1) +/- 1.645*sqrt(0.2*0.8/100+0.1*0.9/100)

--> 0.1 +/- 0.08225

Answer: C. 0.10

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