STAT 200 - Homework 6 Solutions correctly answered

(3 points): 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. Interpret the results. First, we should start off by writing down what we know (always a good place to start). If you write down what you know and what you are trying to solve (purpose of analysis), you can usually determine what method you need to use to solve the problem. n1 = 144,796 n2 = 211,693 x1 = 84,199 x2 = 102,598 C = 1 - α = 1 - 0.9 = 0.1 (remember, the critical region refers to the area in the tail(s), and the confidence interval % refers to the area in the middle) Purpose of Analysis: For this problem, we are to estimate a 90% confidence interval on the difference in proportion of female students taking the biology and calculus AB exam. This difference is given by: p1 – p2 Thus, are computing a confidence interval for the difference between two population proportions. We need to compute the margin of error and add/subtract it from the difference in the sample proportions; we can follow the example on page 267 in the Kozak textbook. i.) State the random variable and the parameters in words. x1 = number of female students taking the biology exam x2 = number of female students taking the calculus AB exam p1 = proportion of female students taking the biology exam