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 Document
Unformatted text preview: sample from a normal population with 3.7, 0.73, 100 x n = = = . Solution. From the Ztable we know that 0.025 1.96 Z = , Therefore the 95% CI for μ is: 3.7 3.7 0.73 1.96 ,0.73 1.96 100 100 + Now we present the derivation of the general formula. 3 Let α be any small positive value less than 1 (*usually less than 0.5), in the above figure, we have: / 2 /2 ( ) 1 P Z Z Z≤ ≤ = /2 /2 /2 / 2 / 2 /2 ( ) 1 ( ) 1 ( ) 1 X P Z Z n P Z X Z n n P X Z X Z n n μ σ≤ ≤ = ≤≤ = ≤ ≤ + = ∴ The 100(1α)% confidence interval for (when 2 is known and the population is normal) is / 2 / 2 , X Z X Z n n + 4...
View
Full Document
 Spring '08
 Zhu,W
 Student's tdistribution, zα

Click to edit the document details