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# lecture8 - Psych 100A Lecture 8 Statistical Inference 1...

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Psych 100A Winter 2010 Lecture 8: Statistical Inference 1.Interval estimate (recap) 2.Hypothesis testing: tests of significance Example Notations and definitions 3.Test for , known 1

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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 t i 900 ( ) f ili “ 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 bl P 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 unknown incomes for this community is unknown, 1. Sampling distribution of mean incomes is normally distributed with mean and ) ( ~ 2 n N x variance 2 /n due to central limit theorem. Or, , 2. Magnitude of chance errors in sample mean when repeatedly drawing a random sample of size 900 from all 25,000 families is 300 \$ 000 9 \$ 900 , n 3 Chance error in sample mean is called 3. Chance error standard error . 3

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