Sample Size Calculations for Confidence Intervals in Statistical Analysis, Study notes of Statistics

Download Sample Size Calculations for Confidence Intervals in Statistical Analysis and more Study notes Statistics in PDF only on Docsity! Stat 4473 – Data Analysis Sample size calculations All the behaviors of confidence intervals discussed earlier still apply. (1) higher confidence levels ] larger margins of error (2) larger samples ] smaller margins of error (3) populations have high variability ] larger margins of error There’s nothing we can do about (3), but if we demand a certain high level of confidence and a certain precision in our interval estimate, we can choose a sufficiently large sample size. Let E = specified margin of error. One sample t-interval for : But, we haven’t taken the sample yet, so we can’t calculate the sample standard deviation, s, nor t* since the df depends on n. • For s, make a good guess or run a small pilot study. • For t*, the common approach is to use the corresponding z* value. • Note: Sample size calculations are never exact. The margin of error you find after collecting the data won’t match exactly the one you specified to find n. The sample size formula depends on quantities that you won’t have until you collect the data, but using it is an important first step. Example An economist wants to estimate the mean income for the first year of work for college graduates who have taken a statistics course. He requires 95% confidence that the sample mean is within $500 of the true population mean. How large should his sample be? Solution: The specified margin of error is $500. So, the sample size should be chosen so that . Suppose a pilot study involving 30 individuals has a standard deviation of $6250. We can’t calculate t*, so we’ll use the corresponding z* value, which is z.975 = 1.96 for 95% confidence. Then, , so the economist should sample 601 individuals. (He can use the 30 he already has and get 571 more.)