Many high school students take the AP tests in different subject areas. In 2005,

Question

Many high school students take the AP tests in different subject areas. In 2005, of the 198544 students who took the Calculus AB exam 97563 of them were Female and 100981 of them were Male. Is there enough evidence that the proportion of Female students taking the Calculus AB exam is different than the proportion of Male students taking the Calculus AB exam? Test at the 5% level of significance. Then, construct a confidence level at the 95% level for the difference in proportion of Females and Males taking the Calculus AB exam.

Explanation / Answer

female = 97563

male = 100981

total = 198544 ,

so p1 = 97563 /198544 and p2 = 100981/198544

p1 =0.49 , p2 = 0.51

pooled sample

p = (p1 * n1 + p2 * n2) / (n1 + n2) = (0.49* 97563+ 0.51*100981)/(198544) = 0.50

standard error is

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }

sqrt{ 0.5 * ( 1 - 0.5 ) * [ (1/97563) + (1/100981) ] } =0.0022

now

z = (p1 - p2) / SE

z =(0.49-0.51) /0.0022

= -9.09

now we check the p value in the z table

the p value is almost zero. Hence we can say that there is a difference in the proportion for females and males

the confidence interval is given as

p+-z*SE , z is 1.96 for the 95% confidence interval

0.50 +-1.96*0.0022

solving this for negative and positive signs , we get

0.495 , 0.504

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