ESBE4eAISEsm11 - Chapter 11 Statistical Inference about...

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Chapter 11 Statistical Inference about Means and Proportions with Two Populations Learning Objectives 1. Be able to develop interval estimates and conduct hypothesis tests about the difference between the proportions of two populations. 2. Know the properties of the sampling distribution of the difference between two proportions () pp 12 . 3. Be able to conduct a goodness of fit test when the population is hypothesized to have a multinomial probability distribution. 4. For a test of independence, be able to set up a contingency table, determine the observed and expected frequencies, and determine if the two variables are independent. 5. Understand the role of the chi-square distribution in conducting tests of goodness of fit and independence. Solutions: 11 - 1 This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied, or distributed without the prior consent of the publisher.
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Chapter 11 1. a. 1 pp 2 = .48 - .36 = .12 b. 112 2 12 . 0 5 (1 ) ) pppp ppz nn −− −± + .48(1 .48) .36(1 .36) .12 1.645 400 300 ±+ .12 ± .0614 (.0586 to .1814) c. .48(1 .48) .36(1 .36) .12 1.96 400 300 .12 ± .0731 (.0469 to .1931) 2. a. 11 2 2 200(.22) 300(.16) .1840 200 300 np p + + == = ++ () .22 .16 1.70 .1840 1 .1840 1 200 300 z ⎛⎞ −+ ⎜⎟ ⎝⎠ = p - value = .5000 - .4554 = .0446 b. p -value .05; reject H 0 . 3. 1 p = 220/400 = .55 2 p = 192/400 = .48 b. 12. 0 2 5 ) ) + .55(1 .55) .48(1 .48) .55 .48 1.96 400 400 + .07 ± .0691 (.0009 to .1391) 7% more executives are predicting an increase in full-time jobs. The confidence interval shows the difference may be from 0% to 14%. 4. a. 1 p = 150/250 = .46 Republicans 2 p = 98/350 = .28 Democrats b. 1 2 = .46 - .28 = .18 Republicans have a .18, 18%, higher participation rate than Democrats. 11 - 2 This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied, or distributed without the prior consent of the publisher.
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Statistical Inference about Means and Proportions with Two Populations c. 1222 .025 12 (1 ) ) pppp z nn −− + .46(1 .46) .28(1 .28) 1.96 .0777 250 350 += d. Yes, .18 ± .0777 (.1023 to .2577) Republicans have a 10% to 26% higher participation rate in online surveys than Democrats. Biased survey results of online political surveys are very likely. 5. a. p 1 = 256/320 = .80 b. p 2 = 165/250 = .66 c. 1 pp 2 = .80 - .66 = .14 112 2 .025 ) ) .14 z ±+ .80(1 .80) .66(1 .66) .14 1.96 320 250 .14 ± .0733 (.0667 to .2133) 6. a. p 1 = 742/924 = .803 b. p 2 = 714/841 = .849 c. H 0 : p 1 - p 2 0 H a : p 1 - p 2 < 0 Support for H a will show p 2 > p 1 which indicates an improvement in on-time performance. d. 11 2 2 742 714 .8249 924 841 np p + + == = ++ () .803 .849 2.54 .8249 1 .8249 1 924 841 z ⎛⎞ −+ ⎜⎟ ⎝⎠ = p -value = .5000 - .4945 = .0055 Reject H 0 . Conclude on-time performance has improved. 11 - 3 This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied, or distributed without the prior consent of the publisher.
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Chapter 11 7. a. H 0 : p 1 - p 2 = 0 H a : p 1 - p 2 0 p 1 = 63/150 = .42 2 p = 60/200 = .30 11 2 2 12 63 60 .3514 150 200 np p nn + + == = ++ () .42 .30 2.33 .3514 1 .3514 1 150 200 pp z ⎛⎞ −+ ⎜⎟ ⎝⎠ = p -value = 2(.5000 - .4901) = .0198 p -value .05, reject H 0 . There is a difference between the recall rates for the two commercials.
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This note was uploaded on 05/26/2010 for the course ACC 251 taught by Professor Carl during the Winter '09 term at University of Central Arkansas.

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ESBE4eAISEsm11 - Chapter 11 Statistical Inference about...

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