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Unformatted text preview: 2 of 7 1.2 Confidence intervals for x z / 2 is z-score with / 2 area to the right . CLT: x is normally distributed with x if either (1) x is normal or (2) n > 30. Poor sampling leads to useless and potentially misleading results! 1.2 Confidence intervals for x USE Often used to answer: 1. What is a reasonable estimate for the population mean? 2. How much variability is there in the estimate for the population mean? 3. Does a given target value fall within the confidence interval? COMPUTATION Confidence interval for when is known. Definition 1.1 Requirements : (1) Simple random samples, (2) CLT applies ( x nor- mal or n > 30). x E (1) where E = z / 2 x (2) and x = n (3) Confidence interval for when is unknown. Definition 1.2 Requirements : (1) Simple random samples, (2) CLT applies ( x nor- mal or n > 30). Just like before except: E = t / 2 x (4) and x = s n (5) Since we also have to estimate x (hence the hat), a margin of error is associated with x so the distribution of x should be broader than when is known. Student t distribution. Definition 1.3 Anthony Tanbakuchi MAT167 Estimating a population mean 3 of 7 A bell shape symmetrical distribution that describes t = x- x (6) with increasing dispersion (variation) as the sample size decreases in terms of the degrees of freedom : df = n- 1 (7) Think of the t distribution as the z distribution but with an ad- justed standard deviation that increases for smaller sample sizes to...
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- Spring '11