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-π ) ≥ 10. Since we don’t know π , we need np and n (1-p ) ≥ 10. When testing the proportion: H0 : π = π0 vs. H A : π ≠ π0 The TS: 000(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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