1. Interval estimates•How accurate are the point estimates?Example: Suppose a city manager in Los Angeles wants to know the mean income () of 25,000 families living in South Los Angeles. She i ti900 ( )fili“ t d” d interviews 900 (n)families “at random” and finds that the sample mean = $14,400. Based on past study, she knows that the population SD () of incomes equals $9,000.P blP t “ i t k ” b th Problem:Put a “give or take” number on the point estimator (ie, the sample mean).x?2
Solution:Although the exact distribution of incomes for this community is unknownincomes for this community is unknown,1. Sampling distribution of mean incomesis normally distributedwith mean and )(~2nNxvariance 2/n due to central limit theorem. Or, ,2. Magnitude of chance errorsin sample meanwhen repeatedly drawing a random sample of size 900 from all 25,000 families is300$0009$900,n3Chance errorin sample meanis called 3. Chance errorstandard error.3
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