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 DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Just rearrange margin of error to get sample size. 19 n p p z e ) 1 ( /2) ( = α n p p z p ) 1 ( ) 2 / ( ± α 2 2 /2) ( ) 1 ( e p p z n = α Don’t know proportion: Make a guess p is unknown Can be estimated with a pilot sample Use prior knowledge You may know that 2% to 7% of all accounts receivables have errors. Use p = 0.07 (value closer to ½) You may know that service availability is between 98% to 99.9%. Use p = .98. Are you clueless? Use p = .50? Gives too many observations 20 Example: Election polling Polling for presidential election between 2 candidates 95% confidence interval Margin of error = + 2% Guess at proportion = 0.5 n = n = [1.962 *.5(.5)]/(.02)2 = 2,401 21 2 2 /2) ( ) 1 ( e p p z n = α Example: Election polling Polling for presidential election between 2 candidates 95% confidence interval Margin of error = + 4% Guess at proportion = 0.5 n = [1.962 *.5(.5)]/(.04)2 = 601 22 2 2 /2) ( ) 1 ( e p p z n = α The Business School is designing a new auditorium and is interested in knowing how many people are left handed so that they can allocate enough seating space for them. A random sample of 100 people shows that 25 are lefthanded. 1. Form a 95% confidence interval for the true proportion of left handers 0.25 = 0.25 ± 1.96 * 0.0433 = [0.1651, 0.3349] Example: Lefthanders 23 = = = n p p p ) ˆ 1 ( ˆ error std. ˆ p ˆ σ n p p z p ) ˆ 1 ( ˆ ˆ /2) ( ± α 0433 . 100 75 . * 25 . = 2. How large a sample would be necessary to estimate the true proportion of lefthanders within 3%, with 95% confidence? Recall the result of a pilot study Margin of error (e) = 0.03 Example: Lefthanders 24 = = 2 2 /2 ) 1 ( e p p z n α 25 . ˆ = p 801 03 . 75 . * 25 . 96 . 1 2 2 = 3. There were some questions raised about the pilot study. How large must the sample be if we want the margin of error for a 95% confidence interval to be less than 0.01, regardless of the true value of p? Margin of error (e) = .01 What value of p give you the most conservative estimate? p=0.5 Example: Lefthanders 25 = = 2 2 /2 ) 1 ( e p p z n α 9604 01 . 5 . 96 . 1 2 2 2 = Important Note – Finite Population Correction Factor Inference presented in these slides assume that the number in the population is very large (infinite). If your sample is larger than 5% of the population, use finite sample correction. 26 where N = population size, n = sample size σ x = σ X n N n N 1 σ ˆ p = p (1 p ) n N n N 1 Key learning points: Confidence intervals General form of a confidence interval: Point estimate + margin of error Margin of error depends on: Confidence level, (1α)*100%, which determines z or t Standard deviation of population Sample size, n Means, σ known or unknown Proportions Finding required sample size for a specified margin of error. 27...
View
Full Document
 Fall '12
 StephenD.Joyce
 Normal Distribution, Standard Deviation, σp

Click to edit the document details