lab4 - Confidence Intervals Allows a statement of...

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1 Confidence Intervals • Allows a statement of confidence about the estimate of the population parameter. • If you were to take a large number of samples, and calculate the CI for each sample, then about 95% (or 99%, if that’s the CI) of them would contain the parameter value. x x x x x x x x σ + µ σ σ + µ σ 58 . 2 58 . 2 : CI % 99 96 . 1 96 . 1 : CI % 95 • The mean score for high school students on an achievement exam is 475 with . You randomly sample 10 students from CPS and obtain a mean of 480 • Given , find the 95% confidence interval for the mean. – First, calculate the standard error, 10 , 10 480, X = = σ = n 10 3.162 10 x n σ == = () 95% CI: 1.96 1.96 480 1.96(3.162) 480 1.96(3.162) 480 6.198 480 6.198 473.802 486.198 .95 xx C µσ µ ≤≤ + −≤ + + = 99% CI: 2.58 2.58 480 2.58(3.162) 480 2.58(3.162) 480 8.158 480 8.158 471.842 488.158 .95 C + + + = 10 = • Calculate the 95% CI with a sample of 100, assuming the same sample mean. Online demonstration - http://www.ruf.rice.edu/~lane/stat_sim/conf_interval/ 1 100 10 : error, standard the affects This x = = σ = σ σ n x 95% CI: 1.96 1.96 480 1.96(1) 480 1.96(1) 478.04 481.196 .95 C + + = Types of errors Good
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This note was uploaded on 07/17/2008 for the course PHYS 321 taught by Professor Zandt during the Spring '05 term at Ohio State.

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lab4 - Confidence Intervals Allows a statement of...

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