You will be asked to answer ONE question that I’ll pick at random from the following two-question pool.

You will be asked to answer ONE question that I’ll pick at random from the following two-question pool. Each question has multiple parts; be SURE to use the letters, such as (a), (b), and (c), in delineating parts of your answers. If you SKIP one of the parts of a question, I have no choice but to give you a zero for that part. Also, remember that I will change the numbers for each questions; the numbers provided below are ONLY examples.

The exam will begin at 5:35 and end at 6:15. That means you will have 40 minutes for the exam. Prepare answers that you can write in LESS than 40 minutes. (I.e., do NOT come in with answers that will require more than 45 minutes; do NOT come without first planning your answers—I have seen students not plan, write only a page or two, and then claim they “just didn’t have enough time. Don’t take that risk.) You will write your answer in a blue book that you provide (with only the last 4 digits of your UB student ID as identification, NO NAMES, please—one point subtracted from total score for those writing names), with no calculator, no notes, and no access to a book. Please bring a clean copy of these questions to the exam.

1. Demonstrate your understanding of sampling distributions.Presuming a population with anormal distribution with a mean of 100 and a standard deviation of 20, (a) draw a sampling distribution for a sample size of n=1; then drawn one of a sample size of n=4; then draw one with a sample size of n=25. Explain (b) the differences that result from the different sample sizes—why there are differences and what they mean. Then (c) calculate what a z-score of 1.0 (i.e., the number that is one standard error above the mean) would mean for each of these three graphs and explain what dividing the distribution in terms of scores above 1.0 (i.e., all scores that are at least one standard error above the mean) might mean for us (what is similar about scores above a z-score of 1.0 for the three sample sizes; what is different?).

1. Calculate a confidence interval for a population average. Begin with the scenario above and by (a) assuming that your sampling of 100 students revealed a mean of 90 on this test and a standard deviation of 20 (not the standard error—the standard error is different and must be calculated from the standard deviation), calculate a 95% confidence interval (assuming that 2.0 is the appropriate t-value for this analyses). Then, (b) draw a graph showing your sample mean and the two sampling distributions that, in effect, define your confidence interval. Finally, (c) explain what this confidence interval tells us.

Extra Credit (10 points possible)

1. Demonstrate your understanding of direct inference with a normal distribution by first (a) drawing a normal distribution with a mean of 100 and a standard deviation of 20. Then, (b) assuming this curve represents test scores, what percent of the students score between 80 and 120 on the test?; what percent score above 140 on the test?; what percent score below 80 on the test? After this, (c) explain the advice you would give a principal concerned with budgeting regarding the number of her 1000 students will need tutoring, costing $100 per student, as required for people scoring below 60 on the test.