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Unformatted text preview: PSTAT 120B  Probability & Statistics Class # 082 Sample size and CIs Jarad Niemi University of California, Santa Barbara 19 May 2010 Jarad Niemi (UCSB) Sample size and CIs 19 May 2010 1 / 14 Class overview Announcements Announcements Homework Homework 6 due Monday, 24 May @ 4pm in SH 5521 Midterm II #6 was incorrect in the answer key, so if you have answer c and have it marked incorrect, see me. Jarad Niemi (UCSB) Sample size and CIs 19 May 2010 2 / 14 Class overview Goals Calculating Type II error probabilities Sample size of z tests Relationship to confidence intervals Jarad Niemi (UCSB) Sample size and CIs 19 May 2010 3 / 14 Sample size Review Largesample αlevel hypothesis tests H : θ = θ H a : θ > θ (uppertail alternative) θ < θ (lowertail alternative) θ 6 = θ (twotailed alternative) Test statistic : Z = ˆ θ θ σ ˆ θ Rejection region : z > z α (uppertail RR) z < z α (lowertail RR)  z  > z α/ 2 (twotailed RR) Jarad Niemi (UCSB) Sample size and CIs 19 May 2010 4 / 14 Sample size Review Any kind of decision you make under uncertainty can have 4 possible outcomes. H True False Test result Reject H Type I error True positive Do not reject H True negative Type II error α = P(type I error) β = P(type II error) 1 β = power of the test Jarad Niemi (UCSB) Sample size and CIs 19 May 2010 5 / 14 Sample size Example Exercise 10.34) A random sample of 500 measurements on the length of stay in hospitals had sample mean 5.4 days and sample standard deviationstay in hospitals had sample mean 5....
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This note was uploaded on 01/10/2011 for the course STAT 120B taught by Professor Bennett during the Fall '09 term at UCSB.
 Fall '09
 Bennett
 Statistics, Probability

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