Lecture10

# Lecture10 - March 12th 1 Sample size estimation based on...

This preview shows pages 1–4. Sign up to view the full content.

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

View Full Document

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

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

Unformatted text preview: March 12th 1. Sample size estimation based on the large sample C.I. for p From the interval 2 2 ˆˆˆˆ (1 ) (1 ) ˆˆ , p p p p p Z p Z n n α α --- ⋅ + ⋅ 2 ˆˆ(1 ) lengh of your 100(1 )% CI 2 p p L Z n α α- =- = × ⋅ ˆ , , L p α are given and we are interested in sample size n . Therefore, 2 2 2 2 2 2 2 2 2 1 1 4( ) 1 ˆˆ 4( ) (1 ) ( ) 2 2 Z Z p p Z n L L L α α α - - = ≤ = (When 1 ˆ 2 p = , it has the maximum value.) Example. ˆ 0.02, 0.05, 0.54 ? L p n α = = = ⇒ = Example. ˆ 0.02, 0.05, 0.5 ? L p n α = = = ⇒ = 2. Sample size calculation for p based on the maximum error E . Definition. ˆ ( ) 1 P p p E α- ≤ = - We want to estimate p within E with a probability of (1 ) α- . Derive the formula for n 1 ˆ ( ) 1 ˆ ( ) 1 ˆ ˆ ( ) 1 and Z = ~ (0,1) ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ (1 ) (1 ) (1 ) (1 ) : ( ) 1 ˆ ˆ ˆ ˆ (1 ) (1 ) P p p E P E p p E E p p E p p P N p p p p p p p p n n n n E E Thus P Z p p p p n n α α α α- ≤ = -- ≤- ≤ = ---- ≤ ≤ = ------ ≤ ≤ = --- & 2 ˆ ˆ (1 ) E c Z p p n α = =- 2 2 2 2 2 2 ˆ ˆ ( ) (1 ) ( ) 4 Z p p Z n E E α α- ∴ = ≤ ⋅ Recall we also derived n based on L- the length of the 100(1 ) α- % large sample confidence interval for p . Their relationship is 2 L E = ⋅ ˆ ( ) 1 ˆ ( ) 1 ˆˆ ( ) 1 ˆˆ ( ) 1 P p p E P E p p E P E p p E p P p E p p E α α α α- ≤ = -- ≤- ≤ = --- ≤ - ≤- = -- ≤ ≤ + = - 2 ∴ The 100(1 ) α- % confidence interval for p is [ ] ˆˆ , p E p E- + ....
View Full Document

## This note was uploaded on 11/14/2010 for the course AMS 312 taught by Professor Zhu,w during the Spring '08 term at SUNY Stony Brook.

### Page1 / 9

Lecture10 - March 12th 1 Sample size estimation based on...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online