Download Practice Problems with Solution - Introductory Biostatistics | PUBHLTH 540 and more Exams Biostatistics in PDF only on Docsity! PubHlth 540 Introductory Biostatistics Page 1 of 3 Unit 6 – Estimation Week #9 - Practice Problems SOLUTIONS The results of IQ tests are known to be normally distributed. Suppose that in 2007, the distribution of IQ test scores for persons aged 18-35 years has a variance σ2 = 225. A random sample of 9 persons take the IQ test. The sample mean score is 115. 1. Calculate the 50%, 75%, 90% and 95% confidence interval estimates of the unknown population mean IQ score. Answer: 50% CI (111.6 , 118.4) 75% CI (109.2, , 120.8) 90% CI (106.8 , 123.2) 95% CI (105.2 , 124.8) Solution: Let the random variable X = IQ test result assumed normal with: μ unknown σ2 = 225, known σ = 15, known Confidence interval estimate of the unknown mean is given by: estimate + { critical value} { se of estimate} where, estimate = observed sample mean = 115 critical value = (1 - α /2)100th percentile Normal(0,1) se of estimate = standard error of sample mean = 225 / 9 = 15 / 3 = 5 …\docu\wk9_solutions.doc PubHlth 540 Introductory Biostatistics Page 2 of 3 For 50% confidence interval estimate: 1 - α = ( 1 - 0.50 ) = 0.50 α/2 = 0.50 / 2 = 0.25 Therefore want ( 1 - .25)100th or 75th percentile = 0.6745 The required confidence interval estimate is thus, estimate + { critical value} { se of estimate} = 115 + { 0.6745 } { 5 } = ( 111.6 , 118.4 ) For 75% confidence interval estimate: 1 - α = ( 1 - 0.25 ) = 0.75 α/2 = 0.25 / 2 = 0.125 Therefore want ( 1 - .125)100th or 87.5th percentile = 1.1505 The required confidence interval estimate is thus, estimate + { critical value} { se of estimate} = 115 + { 1.1505 } { 5 } = ( 109.2 , 120.8 ) For 90% confidence interval estimate: 1 - α = ( 1 - 0.10 ) = 0.90 α/2 = 0.10 / 2 = 0.05 Therefore want ( 1 - .05)100th or 95th percentile = 1.645 The required confidence interval estimate is thus, estimate + { critical value} { se of estimate} = 115 + { 1.645 } { 5 } = ( 106.8 , 123.2 ) For 95% confidence interval estimate: 1 - α = ( 1 - 0.05 ) = 0.95 α/2 = 0.05 / 2 = 0.025 Therefore want ( 1 - .025)100th or 97.5th percentile = 1.96 The required confidence interval estimate is thus, estimate + { critical value} { se of estimate} = 115 + { 1.96 } { 5 } = ( 105.2 , 124.8 ) …\docu\wk9_solutions.doc
