Confidence Intervals - Introductory Statistics - Lecture Notes, Study notes of Mathematical Statistics

Download Confidence Intervals - Introductory Statistics - Lecture Notes and more Study notes Mathematical Statistics in PDF only on Docsity! Stat 366 Lab 10 Problems (November 16, 2006) page 1 TA: Yury Petrachenko, CAB 484, yuryp@ualberta.ca, http://www.ualberta.ca/∼yuryp/ Confidence Intervals 8.39 Let Y1, Y2, . . . , Yn denote a random sample of size n from a population with a uniform distribution on the interval (0, θ). Let Y(n) = max(Y1, Y2, . . . , Yn). Let U = (1/θ)Y(n). (a) Show that U has distribution function FU(u) =    0, u < 0, un, 0 ≤ u ≤ 1, 1, u > 1. (b) Because the distribution of U does not depend on θ, U is a pivotal quantity. Find a 95% lower confidence bound for θ. Large-Sample Confidence Intervals 8.49 Should professional athletes be tested for drugs? Reporting on this question, the Orlando Sentiel (October 31, 1985) noted that Donald Fehr, executive director of the Major League Baseball Player’s Association, “criticized mandatory testing as being unnecessary.” The public does not seem to agree. A Washington Post–ABC News survey found that 73% of 1506 people interviewed favored drug tests for professional athletes; 68% agreed that professional athletes discovered to be using drugs should be banned or suspended from professional sports on the first offence. (a) Find a 95% confidence interval for the percentage of the public that favors drug tests for professional athletes. (b) Upon what assumptions is your confidence interval in (a) based? Selecting the Sample Size 8.62 Suppose that you want to estimate the mean pH of rainfalls in an area that suffers from heavy pollution due to the discharge of smoke from a power plant. Assume that σ is in the neighborhood of .5 pH and that you want your estimate to lie within .1 of µ with probability near .95. Approximately how many rainfalls must be included in your sample (one pH reading