Formulas ST 200 II

Formulas ST 200 II - Sampling Distribution Proportion:...

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Unformatted text preview: Sampling Distribution Proportion: Mean: If n is large then p is approximately normal N ^ p, pq n , n If population is normal (or n is large) then x is (approximately) normal N Confidence Intervals 1. One-proportion z-interval Parameter: Estimator: Standard Error: Margin of Error Confidence interval Needed sample size: p p ^ SE = pq ^^ n (z - z critical value) M E = z SE p ME ^ (z )2 pq ^^ n= M E2 p1 - p2 p1 - p2 ^ ^ SE = p2 q2 ^ ^ p1 q1 ^ ^ + n1 n2 2. Two-proportion z-interval Parameter: Estimator: Standard Error: Margin of Error Confidence interval M E = z SE (^1 - p2 ) M E p ^ (z - z critical value ) 3. One-sample t-interval Parameter: Estimator: Standard Error: Margin of Error Confidence interval x s SE = n M E = t SE n-1 x ME (t - t critical value, df = n - 1) 1 Significance Tests 1. One-proportion z-test Null Hypothesis: Standard Deviation: Test statistic: Model under H0 : P-value: H0 : p = p0 SD = p0 q0 n (^ - p0 ) p z= SD standard normal (z) Test Lower-tailed Upper-tailed Two-sided 2. Two-proportion z-test Null Hypothesis: Pooled p ^ Pooled Standard Error: Test statistic: Model under H0 : P-value: H0 : p1 = p2 Success1 + Success2 n1 p1 + n2 p2 ^ ^ ppooled = ^ = n1 + n2 n1 + n2 SEpooled = z= (^1 - p2 ) p ^ SEpooled ppooled qpooled ^ ^ ppooled qpooled ^ ^ + n1 n2 HA HA : p < p0 HA : p > p0 HA : p = p0 P-value P (z < z0 ) P (z > z0 ) 2P (z < -|z0 |) ( z0 - the observed value ) standard normal (z) Test Lower-tailed Upper-tailed Two-sided HA HA : p1 < p2 HA : p1 > p2 HA : p1 = p2 P-value P (z < z0 ) P (z > z0 ) 2P (z < -|z0 |) ( z0 - the observed value ) 3. One-sample t-test for the mean Null Hypothesis: Standard Error: Test statistic: Model under H0 : P-value: H0 : = 0 s SE = n x - 0 tn-1 = SE Student's t with df = n - 1 Test Lower-tailed Upper-tailed Two-sided HA HA : < 0 HA : > 0 HA : = 0 P-value P (t < t0 ) P (t > t0 ) 2P (t < -|t0 |) ( t0 - the observed value ) 2 ...
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This note was uploaded on 07/25/2008 for the course STT 200 taught by Professor Dikong during the Summer '08 term at Michigan State University.

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Formulas ST 200 II - Sampling Distribution Proportion:...

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