# JMF-9-07 - Inferences About Proportions Chapter 9 Notes Set 8 Spring 2007 CH Reilly UCF IEMS STA 3032 1 Estimating a proportion x n Assume np 15

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CH Reilly UCF - IEMS - STA 3032 1 Inferences About Proportions Chapter 9 Notes Set 8 Spring 2007

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CH Reilly UCF - IEMS - STA 3032 2 Estimating a proportion n p p z p p n p p z p n p n p n n x p ) ˆ 1 ( ˆ ˆ ) ˆ 1 ( ˆ ˆ : CI % 100 ) 1 ( large. y typicall is 15 ) ˆ 1 ( , 15 ˆ : Assume ˆ 2 / 2 / - + < < - - × - - = α
CH Reilly UCF - IEMS - STA 3032 3 Example – CI for proportion Suppose that 250 UCF students were asked if they think that UCF will be the C-USA football champion next season. Results: 122 students responded that they thought UCF would be the C-USA champion next season. Construct a 90% CI for the proportion of all UCF students who think UCF will rule the C-USA in football.

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CH Reilly UCF - IEMS - STA 3032 4 Example (cont’d.) 540 . 0 436 . 0 052 . 0 488 . 0 250 ) 512 . 0 )( 488 . 0 ( 645 . 1 488 . 0 488 . 0 250 / 122 ˆ < < ± ± = = p p
CH Reilly UCF - IEMS - STA 3032 5 Sample size requirement = = - = 2 2 / 2 2 / 4 1 : ) 5 . 0 ( ve conservati be unknown, is If ) 1 ( E z n p p E z p p n α

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CH Reilly UCF - IEMS - STA 3032 6 Example: sample size Recall the UCF/C-USA football survey. Suppose a maximum error (CI half-width) of 0.01 is desired. How many UCF students should be surveyed?
CH Reilly UCF - IEMS - STA 3032 7 Example (cont’d.)   0099993 . 0 6766 ) 5 . 0 1 )( 5 . 0 ( 645 . 1 : Check 6766 06 . 6765 01 . 0 645 . 1 4 1 2 = - = = = n

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CH Reilly UCF - IEMS - STA 3032 8 Remarks Notice that the sample size does not depend on the size of the population. Consider a U.S. political opinion poll: The stated “margin of error” is what the book calls “E”. We should expect that these results (CI’s) are based on a 95% degree of confidence, unless stated otherwise. When polls report a margin of error of ± 3%, we are being told that the sample size is probably less than 1100 (actually, 1068).
CH Reilly UCF - IEMS - STA 3032 9 Tests for several proportions Suppose that we want to test whether two or more independent binomial populations have the same proportions of successes. There is one sample taken from each population. The sample sizes need not be equal. We will look at two cases: Two populations. Three or more populations.

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CH Reilly UCF - IEMS - STA 3032 10 Two population proportions 2 2 2 1 1 1 2 / 2 1 ) ˆ 1 ( ˆ ) ˆ 1 ( ˆ ˆ ˆ : CI % 100 ) 1 ( n p p n p p z p p - + - ± - × - α
UCF - IEMS - STA 3032 11 Example – 2 basketball players Player 1: 400 FT attempts. 300 FTs made.

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## This note was uploaded on 08/22/2010 for the course STA 3032 taught by Professor Sapkota during the Spring '08 term at University of Central Florida.

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JMF-9-07 - Inferences About Proportions Chapter 9 Notes Set 8 Spring 2007 CH Reilly UCF IEMS STA 3032 1 Estimating a proportion x n Assume np 15

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