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# lecture12 - Psych 100A Winter 2010 ecture 2 tatistical...

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Unformatted text preview: Psych 100A Winter 2010 ecture 2: tatistical Inference Lecture 12: Statistical Inference 1. Hypothesis testing for when 2 is unknown nference n two population means 2. Inference on two population means 3. Estimates of independent groups’ 1- 2 a. Known variances . nknown but equal riance b. Unknown but equal variance 4. Hypothesis testing for 1- 2 5. Inference 2 population ’s: Dependent samples 1 1. Theorem: hypothesis test for , 2 unknown If x 1 , x 2 , …, x n is a random sample from a normal population with unknown variance 2 , en, assuming SRS and normality, then, assuming SRS and normality, O O H : O A H . 1 : versus O O . 3 . 2 n s x t TS O : : 1 , 1 , . 2 . 1 n df O n df O error I type t t if H reject t t if H reject CR 1 , 2 . 3 n df O t t if H reject 2 • Example. In the past, the average number of nursing ome days required by elderly patients before they home days required by elderly patients before they could be released to home care was 17 days. It is hoped that a new program will reduce this figure. Do the following data support the research hypothesis at = 0.05? • Data: 3, 5, 12, 7, 22, 6, 2, 18, 9, 8, 20, 15, 3, 36, 38, 43 • Assumptions: 1. The number of days in nursing home care is . num r f y n nur ng m r normally distributed among elderly patients. 2. SRS of 16 elderly patients 3 • Solution. 1. H O : = 17 days versus H A : < 17 days. 2. Data: days 4 . 15 16 / 247 x omputations days 24 . 13 1 2 n x x s i 3. Computations a. Test score (TS) 16 24 . 13 17 4 . 15 n s x t O b. Critical region: 48 . reject H O if t < -t =0.05,df=15 = -1.753. 4 • Interpretation. • Since t = -0.48 is NOT less than –1.753, do not reject H O at = 0.05, and conclude that there is insufficient evidence to suggest that the new program will reduce the average number of nursing home days. • Do we accept H O ? 5 2. Inference on two population means • To find the effect of a new treatment, we wish to compare at least two groups: • ne with treatment One with treatment • One sans treatment (or treatment #2) xperiment can be designed in two ways: • Experiment can be designed in two ways: 1. Independent (unpaired) samples. Objects selected from population #1 have no bearing on objects selected from population #2 2. Dependent (paired) samples. Each . D p (p ) mp . E object selected from population #1 is naturally or forced paired with an bject selected from population #2 object selected from population #2 6 3. Point estimates of 1- 2 , independent roups groups opulation Population of units If 1- 2 , treatment 1 “better” than treatment 2 Independent lection f - treatment 2 If 1- 2 =0, treatment 1 equals than treatment 2 Inference selection Treatment groups If 1 2...
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## This note was uploaded on 03/15/2010 for the course PSYCHOLOGY 100B taught by Professor Firstenberg,i. during the Winter '10 term at UCLA.

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lecture12 - Psych 100A Winter 2010 ecture 2 tatistical...

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