Download Statistical Inference: Hypothesis Testing and Confidence Intervals and more Exams Statistics in PDF only on Docsity! 1 Stat 428 Name Exam 2 Spring 2009 There are a total of 40 points on this exam. Please read each question carefully and ask me if you have any questions. You cannot get full credit unless you show your work. Partial credit will be granted based on worked shown. Make sure to show formulas where appropriate. Please clearly mark your final answer for each problem. For each question, make sure to check that all your assumptions are reasonable, that you show all of your work for all the steps of the procedure that you are using, and to state your conclusions in context. 1) (10 points) A random sample of 121 lightning flashes in a certain region resulted in a sample average radar echo duration of 0.81 sec and a sample standard deviation of 0.34 sec. Report an approximate 99% upper bound for the true average echo duration . We must start by assuming that the radar echo durations of lightning flashes are independently distributed according to the same (population) distribution. We are told that we have a random sample, so independence is reasonable. Although we are not told that the distribution of radar echo duration is Normal, we can use the t distribution since our sample size is large enough for the central limit theorem to come into play. We have that = 0.01, so , 1 0 .01,120n t t = 2.358. , 1 0.34 0.81 2.358 0.81 0.073 0.883 121 n s x t n We are approximately 99% confident that the population average radar echo duration is no more than 0.883 seconds. 2 2) (6 points) Surgeons examined their results to compare two methods for a surgical procedure used to alleviate pain on the outside of the wrist. A new method was compared with the traditional “freehand” method for the procedure. Of 45 operations using the “freehand” method, 3 were unsuccessful. The following is Minitab output for the exact confidence interval for the proportion of operations that are unsuccessful with the “freehand” method. Test and CI for One Proportion Sample X N Sample p 95% CI 1 3 45 0.066667 (0.013965, 0.182684) a) (4 points) Interpret the interval in context. We are at least 95% confident that the true proportion of unsuccessful “freehand” procedures is between 0.014 and 0.183. b) (2 points) Explain why we would not choose to use the Wilson Score interval in this situation. The Wilson Score Interval is based on a Central Limit Theorem approximation of the distribution of the sample proportion as a normal distribution. Since we only have 3 “successes,” the sample size is not large enough to justify this approximation (rule of thumb: at least 10 successes and at least 10 failures). Thus, we cannot use the Wilson Score Interval.
