Lecture 9

# Lecture 9 - Probability and Statistics in the Life...

This preview shows pages 1–6. Sign up to view the full content.

Probability and Statistics in the Life Sciences (Spring 2010) AMS 110.02 Lecture 9 (chap6) Donghyung Lee

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

View Full Document
Section 6.6 Confidence Interval for a Population Proportion Normal approximation to binomial distribution (Section 5.5) (a) If n is large, then the binomial distribution can be approximated by a normal distribution with n: the sample size ( # of independent trials) p: the population proportion (the probability of success in each independent trial) (b) If n is large, then the sampling distribution of can be approximated by a normal distribution with (1 ) np np p μ σ = = - ˆ p ˆ ˆ (1 ) p p p p p n = - =
Section 6.6 Confidence Interval for a Population Proportion Wald confidence interval (1) If n is large, ~ ( , ); : # X Bin n p X of success ( 29 ( 29 2 2 2 2 2 ~ ( , (1 ) ) ( . . ) (1 ) (1 ) ˆ ~ ( , ) ( , ) ˆ ~ (0,1 ) ˆˆ (1 ) X N np np p by C LT np p X np p p p N N p n n n n p p Z N p p n - - - = = - = -

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

View Full Document
Section 6.6 Confidence Interval for a Population Proportion Wald confidence interval (2) /2 /2 /2 /2 /2 /2 /2 /2 /2 ( ) 1 ˆ ( ) 1 ˆˆ (1 ) ˆˆˆˆ (1 ) (1 ) ˆ ( ) 1 ˆˆˆˆ (1 ) (1 ) ˆˆ ( ) 1 ˆˆ (1 ) ˆ 100(1 )% . . P z Z z p p P z z p p n p p p p P z p p z n n p p p p P p z p p z n n p p Wald C I is p z n α - = - - -≡ = - - - - = -≡ - = - - - = -≡♠ + = - - -
Section 6.6 Confidence Interval for a Population Proportion Wald confidence interval (3) Most books present the Wald confidence interval, since it is much more simple in form. However, the Wald confidence interval has poor coverage properties: A nominal 95% Wald confidence

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.

{[ snackBarMessage ]}

### Page1 / 17

Lecture 9 - Probability and Statistics in the Life...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online