Week 10 Wed Nov 3 - 1 Posted before class WEEK 10 – Wed...

Info iconThis preview shows pages 1–4. 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 DocumentRight Arrow Icon

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

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

Unformatted text preview: 1 Posted before class WEEK 10 – Wed, Nov 3 Correct Formulas for Sample-Size Determination The equations that should be solved when using simple random sampling from a population of size N are n N n N z B 1 2 / (*) n p p N n N z B ) 1 ( 1 2 / (**) with results 1 / / 2 2 2 2 / 2 2 2 2 / B z N B N z n c (6-10c) 1 / ) 1 ( / ) 1 ( 2 2 2 / 2 2 2 / B p p z N B N p p z n c (6-11c) where we have chosen to label the correct sample size as n c . There is a better way to state these results : To evaluate (6-10c) or (6-11c), first calculate n b using the book’s (6- 10) or (6-11) and then plug the result into (***). N n n n b b c ) 1 ( 1 . (***) 2 Example . CI estimation of μ. Suppose the population size is N = 854, σ is unknown, desired margin of error is B = 2, and desired confidence level is 99%. Suppose σ = 10 is used for planning the sample size . We use (6-10c). We find n b = 165.89 and then by (***) we find n c = 139.1. This suggests that the sample size should be n = 140 for a simple random sample selected from the population of size N = 854.. Hypothetical Implementation. Take n = 140 and use the t-interval estimate of μ with 139 df once the data are in. Using the book’s Table 3 and the conservative approach to finding the t-multiplier t .005 , we would use the multiplier t .005 = 2.617 (120 df ). With some hypothetical data x = 76.4, s = 10.3, the t-interval estimate for the population mean μ is ) 140 / 3 . 10 ( 1 854 140 854 617 . 2 4 . 76 / 1 005 . n s N n N t x which evaluates to 1 . 2 4 . 76 . We can present the interval estimate as 74.3 < μ < 78.5 with 99% confidence. Note that the realized margin of error 2.1 is a little larger than the planned B = 2. Discuss. Example . CI estimation of p. Population size N = 253, desired margin of error B = .04, 95% confidence level, p = .5 for planning purposes. Then n b = 600.25 and n c = 178.2. Take n = 179. 3 Insurance Company (IC) Example (a real case) . The IC conducted an audit of N = 4,492 billings from a medical device supplier that it had received and paid over a period of time. The IC used a simple random sample of size n = 188 billings and audited the sample billings. Pages IC-1 and IC-2 to follow provide the information IC provided to attorneys when asked how it came to the sample size n = 188. attorneys when asked how it came to the sample size n = 188....
View Full Document

This note was uploaded on 02/01/2011 for the course STAT 315 taught by Professor Dennisgilliland during the Summer '10 term at Michigan State University.

Page1 / 12

Week 10 Wed Nov 3 - 1 Posted before class WEEK 10 – Wed...

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

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