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# Section7.1posted - STOR 155 Section 2 Thursday Section 7.1...

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Unformatted text preview: STOR 155, Section 2 Thursday, April 15, 2010 Section 7.1 For the standard Normal distribution, z * = 1.96 is a critical value , because A 95% confidence interval for μ is x ± 1.96 / n σ √ , and In a 2-sided hypothesis test, if z = 1.96 or -1.96, then the P-value is .05. 7.1 Inference for the mean of a population Background: Critical values of distributions _ [ If z = 1.96 and H a is μ>μ , the P- value is .025. If z = -1.96 and H a is μ<μ , the P- value is also .025. ] • As on the previous slide, z* = 1.96 is a critical value : – Its upper tail probability is .025 , so • a 95% confidence interval for μ is x ±1.96 / n, σ √ • the P-value for a 2-sided test is .05 if z = ±1.96. • Another critical value: z* = 1.65 . – Upper tail probability is .05 , so • a 90% confidence interval for μ is x ± 1.65 / n σ √ • the P-value for a 2-sided test is .10 if z = ±1.65 . • Another critical value: z* = 2.58 . – Upper tail probability is .005 , so • a 99% confidence interval for μ is x ± 2.58 / n σ √ • the P-value for a 2-sided test is .01 if z = ± 1.65 . 7.1 Inference for the mean of a population Background: Critical values of distributions _ _ _ 7.1 Inference for the mean of a population: Some critical values of the standard Normal distribution Upper tail probability, p 0.10 0.05 0.025 0.01 0.005 Confidence level, C 80% 90% 95% 98% 99% Critical value, z * 1.28 1.65 1.96 2.33 2.58 C = 1 – 2 p p = ½(1 – C ) 7.1 Inference for the mean of a population: How a table of critical values (rather than Table A) is used (Example 2) Upper tail probability, p 0.10 0.05 0.025 0.01 0.005 Confidence level, C 80% 90% 95% 98% 99% Critical value, z * 1.28 1.65 1.96 2.33 2.58 Testing H 0 : µ = µ vs. H a : µ ≠ µ ....
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Section7.1posted - STOR 155 Section 2 Thursday Section 7.1...

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