lecture6note - Psych 100A Winter 2009 Lecture 6: Normal...

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1 Lecture 6: Normal Distribution and Statistical Inference Psych 100A Winter 2009 Normal distribution 1. General properties 2 Standard normal distribution 2. Standard normal distribution 3. Standardization of units 4. Finding areas under normal curves Statistical Inference 1. Statistical inference: techniques 2. Point estimates 1 Example • Is this a binomial experiment? Yes • Fair coin tossed four times. What is the chance of getting exactly 2 heads? 1. n = 4 iid trials (assume coin toss process OK) 2. Dichotomous outcome (“heads, H” or “tails, T”) 3. Pr(H) = Pr(T) = ½, which is constant. 4. Variable = total number of successes (heads) 2 1 st 2 nd Toss: 3 rd 4 th HHTT Solution 1. •Draw a path diagram. HTHT HTTH 1 2 7 6 3 4 5 8 H T H T H T H T H T H T T H H 3 6 THHT THTH TTHH 9 10 15 14 11 12 13 16 H T H T H T H T H T T H H T T 8 16 ) ' 2 Pr( s H 3 Formula: Pr(success) in a binomial experiment • Probability of x successes in n trials of a binomial experiment is x n x p p x n x n successes x ) 1 ( )! ( ! ! ) Pr( •where • n = number of trials • p = probability of success • 1-p = probability of failure • x = number of successes • x! = x(x-1)(x-2)…(2)(1) 4 4. Normal distribution • Special continuous probability distribution 5 Suppose 0 .125 .250 .375 Density 01 23 Number of heads x 0 1 2 3 Pr(x) .125 .375 .375 .125 N=3 N=10 x 0 1 2 3 4 5 Pr(x) .0010 .0097 .0439 .1172 .2051 .2461 0 .125 .250 .375 01 2345678910 Number of heads 6
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2 Suppose 0 .025 .050 .075 .100 .125 Density 0 1 02 03 04 05 0 Number of heads x 0 1 12 15 20 25 Pr(x) .0000 .0000 .0001 .0020 .0418 1123 N=50 .1123 Number of heads N=immense An ideal or normal curve should approximate well the binomial distribution 7 .50 Normal curve deMoivre’s normal curve 2 2 2 1 ) ( x e f 0 .25 - 4- 3 - 2 - 101234 Standard units 8 1. General properties of normal dist. a. Family of continuous probability distributions. A particular member is defined by its center (mean, ) and spread (SD, ).
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lecture6note - Psych 100A Winter 2009 Lecture 6: Normal...

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