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class08-2-handouts

class08-2-handouts - PSTAT 120B Probability Statistics...

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PSTAT 120B - Probability & Statistics Class # 08-2- 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
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Class overview Announcements Announcements Homework Homework 6 due Monday, 24 May @ 4pm in SH 5521 Mid-term 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
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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
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Sample size Review Large-sample α -level hypothesis tests H 0 : θ = θ 0 H a : θ > θ 0 (upper-tail alternative) θ < θ 0 (lower-tail alternative) θ 6 = θ 0 (two-tailed alternative) Test statistic : Z = ˆ θ - θ 0 σ ˆ θ Rejection region : z > z α (upper-tail RR) z < - z α (lower-tail RR) | z | > z α/ 2 (two-tailed RR) Jarad Niemi (UCSB) Sample size and CIs 19 May 2010 4 / 14
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Sample size Review Any kind of decision you make under uncertainty can have 4 possible outcomes. H 0 True False Test result Reject H 0 Type I error True positive Do not reject H 0 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
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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 deviation
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