props_formulas

props_formulas - Formulas for Proportions p (1 p) n 1. The...

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Formulas for Proportions Confidence Interval for π (proportion): / 2 (1 ) p p p z n α - ± 1. The sample proportion, p , estimates the population mean, π , and for large enough samples this interval is sufficient. 2. The margin of error is made of: a. z α /2 gives us the desired confidence level. b. the standard error of p is (1 ) p p p SE n - = since the standard deviation is dependent on π , the parameter we’re having to estimate. c. the sample size, n , which allows us to control the variability of our statistic, p . 3. We must have a random sample so p is unbiased and the standard deviation of p is (1 ) n π - . 4. We are using z -scores, so we must have n π and n (1 ) 10. Since we don’t know π , we need np and n (1 - p ) 10. When testing the proportion: H 0 : π = π 0 vs. H A : π π 0 The TS: 0 0 0 (1 ) p z n - = - Since we have a hypothesized value for π , we use this value in our test statistic. Two sample cases: Confidence Interval for
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