{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture9 - March 5 th Large Sample Confidence interval for...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: March 5 th ( Large Sample ) Confidence interval for a population proportion p Let . . . ~ ( ), 1, , i i d i X Bernoulli p i n = L , please find the 100(1-α)% CI for p. 1) Point estimator : 1 ˆ n i i X p X n = = = ∑ (ex. 1000 n = , ˆ 0.6 p = ) 2) 100(1-α)% C.I. for p <Thm> Central Limit Theorem ( ) (0,1) ( ) n X E X N Var X → ∞- → When n is large enough, we have ( ) ~ (0,1) ( ) X E X Z N Var X- = & Application #1. Inference on μ when the population distribution is unknown but the sample size is large ~ (0,1) / X Z N n μ σ- = & ~ (0,1) / X Z N S n μ- = & (Slutsky’s Theorem) => 100(1 )% α- C.I. for μ /2 S X Z n α ± Application #2. Inference on one population proportion p when the population is Bernoulli(p) *** ( ) ~ (0,1) ( ) X E X Z N Var X- = & 1 1 ( ) ( ) ( ) i i X E X E E X np p n n n = = = ⋅ = ∑ ∑ , ( ~ ( , )) i X B n p ∑ Q 2 2 1 1 (1 ) ( ) ( ) ( ) (1 ) i i X p p Var X Var Var X np p n n n n- = = =- = ∑ ∑ 1 ~ (0,1) (1 ) X p Z N p p n- =- & ˆ ~ (0,1)...
View Full Document

{[ snackBarMessage ]}

Page1 / 4

Lecture9 - March 5 th Large Sample Confidence interval for...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online