This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 2sided hypothesis test, if z = 1.96 or 1.96, then the Pvalue 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 Pvalue for a 2sided 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 Pvalue for a 2sided 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 Pvalue for a 2sided 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 ....
View
Full Document
 Spring '08
 AndrewB.Nobel
 Normal Distribution, Upper tail probability

Click to edit the document details