Chapter14 - CHAPTER 14 Section 14.1 1. a. We reject Ho if...

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439 CHAPTER 14 Section 14.1 1. a. We reject H o if the calculated 2 c value is greater than or equal to the tabled value of 2 1 , - k a c from Table A.7. Since 488 . 9 25 . 12 2 4 , 05 . = c , we would reject H o . b. Since 8.54 is not 344 . 11 2 3 , 01 . = c , we would fail to reject H o . c. Since 4.36 is not 605 . 4 2 2 , 10 . = c , we would fail to reject H o . d. Since 10.20 is not 085 . 15 2 5 , 01 . = c , we would fail to reject H o . 2. a. In the d.f. = 2 row of Table A.7, our 2 c value of 7.5 falls between 378 . 7 2 2 , 025 . = c and 210 . 9 2 2 , 01 . = c , so the p-value is between .01 and .025, or .01 < p-value < .025. b. With d.f. = 6, our 2 c value of 13.00 falls between 592 . 12 2 6 , 05 . = c and 440 . 14 2 6 , 025 . = c , so .025 < p-value < .05. c. With d.f. = 9, our 2 c value of 18.00 falls between 919 . 16 2 9 , 05 . = c and 022 . 19 2 9 , 025 . = c , so .025 < p-value < .05. d. With k = 5, d.f. = k – 1 = 4, and our 2 c value of 21.3 exceeds 860 . 14 2 4 , 005 . = c , so the p-value < .005. e. The d.f. = k – 1 = 4 – 1 = 3; 0 . 5 2 = c is less than 251 . 6 2 3 , 10 . = c , so p-value > .10.
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Chapter 14: The Analysis of Categorical Data 440 3. Using the number 1 for business, 2 for engineering, 3 for social science, and 4 for agriculture, let = i p the true proportion of all clients from discipline i. If the Statistics department’s expectations are correct, then the relevant null hypothesis is , 10 . , 20 . , 30 . , 40 . : 4 3 2 1 = = = = p p p p H o versus : a H The Statistics department’s expectations are not correct. With d.f = k – 1 = 4 – 1 = 3, we reject H o if 815 . 7 2 3 , 05 . 2 = c c . Using the proportions in H o , the expected number of clients are : Client’s Discipline Expected Number Business (120)(.40) = 48 Engineering (120)(.30) = 36 Social Science (120)(.20) = 24 Agriculture (120)(.10) = 12 Since all the expected counts are at least 5, the chi-squared test can be used. The value of the test statistic is ( 29 ( 29 - = - = = allcells k i i i i ected ected observed np np n exp exp 2 1 2 2 c ( 29 ( 29 ( 29 ( 29 57 . 1 12 12 9 24 24 21 36 36 38 48 48 52 2 2 2 2 = - + - + - + - = , which is not 815 . 7 , so we fail to reject H o . (Alternatively, p-value = ) 57 . 1 ( 2 c P which is > .10, and since the p-value is not < .05, we reject H o ). Thus we have no evidence to suggest that the statistics department’s expectations are incorrect. 4. The uniform hypothesis implies that 125 . 8 1 0 = = i p for I = 1, …, 8, so 125 . ... : 80 20 10 = = = = p p p H o will be rejected in favor of a H if 017 . 12 2 7 , 10 . 2 = c c . Each expected count is np i0 = 120(.125) = 15, so ( 29 ( 29 80 . 4 15 15 10 ... 15
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This note was uploaded on 03/30/2008 for the course STAT 211 taught by Professor Parzen during the Spring '07 term at Texas A&M.

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Chapter14 - CHAPTER 14 Section 14.1 1. a. We reject Ho if...

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