STP 231 Study Guide - Midterm Guide: Test Statistic, Confidence Interval, Point Estimation
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Sampling distribution of the sample mean has mean x = and standard deviaiton x = /sqrt(n) Confidence interval formula for one population mean when population standard deviation ( ) is unkown x-bar t /2(s/sqrt(n)) Where x-bar is the point estimate t /2is the critical value correspoinding ot a confidene level of 1- with df. = n-1 t /2(s/sqrt(n)) is the margin of error, denoted by e Confidence interval for the difference between population means with unknown population standard deviations: and df = Important: you may use the smaller of (n1-1) and (n2-1) as an estimation of df. Increasing sample size while keeping the same confidence level decreases the margin of error (narrower confidence interval and higher precision) Increasing the confidence level while keeping the same sample size. 2. increases the margin of error (wider confidence interval and lower precision) Correctly interpreting a confidence interval: the width of a confidence interval is twice the margin of error.
