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Section 7.3

Section 7.3 - 7.3 Large Sample(CI's for and 1 2 Confidence...

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7.3 Large Sample (CI’s) for π and 2 1 μ μ - Confidence interval for proportion A bound on the error of estimation A confidence interval for µ 1 2 Let π = proportion of population having a particular characteristic. A sample of size n is taken and a natural estimate for π is n successes of number = p , where Success = possessing the characteristic. Properties of sampling distribution of the proportion p / n π σ π μ p p ) 1 ( = = If both np and n (1-p) greater than 10, then sampling distribution for proportion is approximately normal. When n is large, z = (1 ) / p n π π π - - ~ N ( 0, 1). Using the earlier approach, 100(1- α )% CI is (we need to solve a Quadratic equation here ) 1

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n z n z n p p c n z c c c z p 2 2 2 2 ) ( 4 ) ( ) 1 ( 2 ) ( 1 + + ± + - where ). 2 1 ( α - = c Assumptions 1. SRS sample 2. Observations independent on each other 3. If sampling without replacement, the sample size n should be no more than 10% of the population. 4. Large “sample size” 10) ) - (1 and 10 ( π n Now ) - (1 100 α % confidence interval (aaproximate) for a population proportion = 2 - 1 c α is n p p p ) 1 ( z c - ± , where c z is a central area critical value for standard normal.
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