Week2A2304 - ADM2304: One Proportion Dr. Suren Phansalker...

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1 ADM2304: One Proportion Dr. Suren Phansalker 1. Sample Proportion: Here and , X~ b(n, p, x) where X is the # of successes and n is the Sample Size. 2. CLT for If then Or, X p n = p 10 np nq > > 2 ,( ) pq pN p p n σ = p ) p p n = (1 ) qp =
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2 • The CLT for the Sample Proportion, states that when the product of the sample size and and sample size and and both products are more than 10, the has a Normal Distribution with mean given by ‘p’ the population proportion and standard deviation given by This theory is very useful if ‘p’ and ‘q’ are known. Please Refer to “Week2B&3BMTB2304”. 3. Example 1 for CLT: Recently, in an election in a foreign country, it was found that when 100 people were checked at random on the voters’ list, 90 seemed to have voted. It was well known from past experience that 80% people generally voted. What can you say about what was found? p q p pq n
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3 Here p = 80% = 0.80 and q = (1 – p) = (1 – 0.80) Thus, q = 0.20 Hence (n p) = 100 (0.80) = 80 > 10, and (n q) = 100 (0.20) = 20 > 10. Hence CLT for Sample Proportion applies. Now Here ,( ) pq pN p p n σ = 0.80(0.20) ( ) 0.0016 0.04 100 p n == = = 90 0.90 X p n =
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4 •T h u s : P[Z > 2.50] = 0.5 – A[z = 2.50] P[Z > 2.50] = 0.5– 0.4938 = 0.0062 ( 6.2 in 1000) This is a rather small probability; all though it is possible, it is not very probable or likeky!
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Week2A2304 - ADM2304: One Proportion Dr. Suren Phansalker...

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