Hypothesis Testing The z-test for Proportions

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$Math 110 Test # 1$

$Calculus 2 for Engineers (Math 124) - Department of Mathematics ...$

2. Collect the data 3. Compute the test statistic z = 4. Make the Decision • Accept H0 if: − z ≤ z ≤ z • Reject H 0 if: x − μ0 x − μ n ≈ n σ s α / 2 α / 2 z < −z z > z 0 α / 2 or The one tailed test α / 2 To test H0 : μ ≤ μ0 (some specified value of μ) against HA : μ > μ0 1. Use the test statistic z = x − μ0 x − μ n ≈ n σ s 2. Use as the Acceptance and Critical Region • Accept H0 if: z ≤ zα / 2 • Reject H0 if: z > z Accept H 0 0 α / 2 zα 0 α Reject H 0 z The one tailed test – other direction To test H0 : (some specified value of μ) against HA : 0 μ μ ≥ μ0 μ < Acceptance and Critical Region • Accept H 0 if: • Reject H 0 if: Test Statistic α Reject H 0 z = z ≥ −z z < −z α / 2 α / 2 x − μ0 x − μ n ≈ n σ s Expect z to be negative if H 0 is false Example: The Acceptance and Critical region: − zα Accept H 0 We are interested in measuring the concentration of lead in water and we want to know if it exceeds the threshold level μ 0 = 10.0 We take n = 40 one-litre samples measuring the concentration of lead. Statistical results: x = 12 . 1 and s = 1. 2 0 0 z 8
Test Statistic z = = x − μ0 x − μ n ≈ n σ s 12. 1 −10. 0 40 = 11. 07 1. 2 Since z is greater than z 0.05 = 1.645 we conclude that the average lead level is significantly higher than 10.0 0 9
Page 1 and 2: Hypothesis Testing To define a stat
Page 3 and 4: α The Test Statistic pˆ − p z =
Page 5 and 6: Performing the Test 1. Decide on α
Page 7: The Data • Let x1 , x2 , x3 , …

Hypothesis Testing The z-test for Proportions

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