Hi all, I teach high school level AP Statistics, and I'm working a problem in AMSCO's "AP Statistics" study guide, by James Bohan, for my students. It's problem number 4 in chapter 6.4 (page 164), entitled "Sampling Distributions of a Difference of Two Proportions." It's multiple choice. The problem is stated as follows:
"A school district had anticipated that the percentages of boys and girls who planned no further education would be the same, approximately 44% for all of the students. Two independent random samples of the seniors at a high school are taken; the first was a sample of 10 boys and the second ws a sample of 25 girls. The boys' sample indicated that 50% of them planned no further education after graduation, while the gurls' sample indicated that only 40% of them planned no further education after graduation. Which of the following is valid for this information?" The solution explanation (in the back of the book, p349) states that "the small sample size indicates that we cannot assume normality, but the formula for the standard deviation is true regardless of the sape of the distribution." I agree with the explantion. What I don't understand is that this seems to contradict the solution, (choice A), which states: "The sampling distribution is approximately normal with mean 0 and approximate standard deviation .1857." It seems to me that the solution assumes a normal distribution, but the explation explicitly states that this can't be assumed. I've searched for online errata, and found none. You're my last hope of looking smart in front of my students tomorrow. ;-) Can someone straighten me out? (I've included the complete set of solutions below, for completeness) Thanks, in advance. -M A) The sampling distribution is approximately normal with mean 0 and approximate standard deviation .1857. B) The sampling distribution is approximately normal with mean .1 and approximate standard deviation .0345 C) No conclusion can be drawn regarding the sampling distribution since the samples are taken from the same population. D) No conclusion can be drawn regarding the sampling distribution since the sample size of the boys' sample is too small E) None of these statements is valid. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
