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lecture8 - Binomial Distribution (nish Ch. 6) Sampling...

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± Binomial Distribution ( nish Ch. 6) ± Sampling Distributions (Ch. 7) ± Distribution of sample means & probability ± Standard error ± Binomial variables are those that have two possible values or categories ± Examples ± Coin Toss: heads/tails ± Gender: Male/Female ± Parity: Odd/Even ± Accuracy: Correct/Incorrect ± Pregnancy: You either are pregnant or you are not pregnant ± Two c a t e go r i e s : A a n d B ± Probability of A= (#Possible As)/(Possible Outcomes)=p(A)= p ± Probability of B= (#Possible Bs)/(Possible Outcomes)=p(B)= q ± p+q=1 ± n = number of observations ± X = number of times A occurs among the n individuals or observations (0 to n) ± The binomial shows the probability associated with each value of x
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± What are A & B? ± p & q? ± n? ± What does X refer to? ± Heads and tails ± p=0.5; q=0.5 ± n = 2 ± X = number of heads in the 2 tosses How many heads? 0 1.25 2.50 3.75 5.00 012 Frequency Number of heads
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As the number of tosses increases, the distribution approximates a normal distribution. As a general rule, the normal approximation is valid when pn and qn > 10 ± If the binomial approximates the normal then we can use the normal distribution to determine probabilities for a binomial variable. ± called the ²normal approximation³ ± But how do we do this? ± Convert to z ± Need " and ± Mean: ± = pn Standard Deviation: ± = z = X ± ± ² z = X ± = X ± pn npq
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± Applying the normal distribution is only an approximation ± The normal distribution is continuous, but the binomial is, by de nition, discrete.
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This note was uploaded on 02/18/2011 for the course PSYCH 5 taught by Professor Collins during the Fall '08 term at UCSB.

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lecture8 - Binomial Distribution (nish Ch. 6) Sampling...

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