Question

In a large midwestern university (the class of entering freshmen is 6000 or more students), an SRS of 100 entering freshmen in 1999 found that 20 finished in the bottom third of their high school class.  Admission standards at the university were tightened in 2000.  In 2001, 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 1999 and 2001, 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 class in 2001 has been reduced, as a result of the tougher admission standards adopted in 2000, compared to the proportion in 1999?  To determine this, you test the hypotheses

H0: p1 = p2, Ha: p1 > p2.

The z-test statistic is approximately 1.98, find the P-value, using a Standard Normal Table or your calculator.

    

	A.	0.0239
	B.	0.0478
	C.	0.4880
	D.	0.9761

Answer 1

= 20/100 = 0.2

= 10/100 = 0.1

The pooled sample proportion(P) = ( * n1 + * n2)/(n1 + n2)

                                                     = (0.2 * 100 + 0.1 * 100)/(100 + 100)

                                                     = 0.15

SE = sqrt(P * (1 - P) * (1/n1 + 1/n2))

     = sqrt(0.15 * (1 - 0.15) * (1/100 + 1/100))

     = 0.0505

The test statistic z = ()/SE

                             = (0.2 - 0.1)/0.0505

                             = 1.98

P-value = P(Z > 1.98)

             = 1 - P(Z < 1.98)

             = 1 - 0.9761

             = 0.0239

Option - A is correct.