Question

Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students who took the biology exam 84,199 of them were female. In that same year, of the 211,693 students who took the calculus AB exam 102,598 of them were female ("AP exam scores," 2013). Estimate the difference in the proportion of female students taking the biology exam and female students taking the calculus AB exam using a 90% confidence level.

Considering it is asking for the "difference" in the proportion, what would the null hypothesis (H0) and the alternative hypothesis be (H1)?

Answer 1

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 not= mu2

where mu1 is population proportion for female students taking the biology exam.

mu2 is population proportion for  female students taking the calculus AB exam.

Assume alpha = level of significance = 10% = 0.1

Now we have to find confidence interval for difference in proportion.

We can find this confidence interval in ti-83 calculator.

steps:

STAT --> TESTS --> B : 2-PropZInt --> ENTER --> Input all the values --> C-level : 90% --> Calculate --> ENTER

90% confidence interval for difference in population proportion is (0.0941, 0.0996)

We are 90% confident that difference in popopulation proportion is lies between 0.0941 and 0.0996.

We can see that population proportion difference = 0 does not lies in confidence interval.

Reject H0 at 10% level of significance.

COnclusion : There is not sufficient evidence to say that population proportion difference is equal to 0.