answer key of chapter 5

answer key of chapter 5 - 5.8 a 5.14 For confidence...

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Unformatted text preview: 5.8 a. 5.14 For confidence coefficient .90 a : 10 and (1,2 __ 05 me Table W _ 9 I F . I , A d 2.05 = 1.645. The confidence interval is: PM I): B, — s x j; zan— = 3.39 i moi = 3.39 i .0466 =9 (3.3434, 3.4366) 1/; W Since the sample size was so large, no assumptions are necessary- We are 90% confident that the mean risk is between 3.3434 and 3.4366. Since: all values included in tile interval exceed 2.5. the rescarchers would conclude that students in these grades exhibit an awareness of risk involved in bicycling. First. we must compute E and s. E=£x=3_0=5 n 6 Ex? _ Ex? 176 ._ (30}2 ' 2 n 6 26_ S: = =.._—52 nel 6—1 5 .s = ‘63 = 2.2804 .90 = .10 and 0112 = .101’2 = .05. From Table VI, For confidence coefficient .90, o: - 1 = S. 135 = 2.015. The 90% confidence interval is: Appendix B, with df = n e- 1 = 6 i + 1051 = 5 i 2.015 12804 = 5 i 1.876 = (3.124, 6.376) — Jr? J3 For confidence coefficient .95. o: = 1 —- .95 = .05 and 1212 = .05i2 = .025. From Table VI, Appendix B, with df z n — 1 = 6 — l = 5, 11025 = 2.571. The 95% confidence interval is: E + (mi 3 5 4; 2.5712'2804 h 1/? J3 = 5 i 2.394 = (2.606, 7.394) For confidence coefficient .99, or = 1 — .99 = .01 and 010 = .01-1'2 = .005. From Table V1, Appendix B. with df = n — 1 = 6 - 1 = 5,1035: 4.032. The 99%.confidence interval is: E i 7.005.: = 5 i 4.032 2230“ = Jr? 1/3 a) For confidence coefficient .90, o: = 1 — .90 = .10 and 0112 = .1012 = .05. From Table VI. Appendix B, with df = n — 1 = 25 — 1 = 24.1.05 =1.711. The 90% confidence interval is: 5 i 3.754 =9 (1.246, 8.754)- } J; 105.2 = 5 1 1.711”304 = 5 i .780 = (4.220, 5.730) ,[n' ¢2s 5.22 b) For confidence coefficient .95, o: = 1 -— .95 = .05 and (132 = .0572 = .025. From Table VI, Appendix B, with (if = n -— l = 25 ~ 1 = 24, {025 = 2.064. The 95%- confidence interval is: E i 1.025% a 5 i 106422804 = 5 i .941 =~ (4.059, 5.941) 77 1/25 For confidence coefficient .99. o = 1 — .99 = .01 and of? = .011’2 = .005. From Table VI, Appendix B, with df = n —— 1 = 25 — 1 = 24, {005 = 2.797. The 99% confidence interval is: 5 = 5 i 2.797 2-2804 = 5 i 1.276 = (3.724, 6.276) i+t ._ .oos‘l/F «.25— Increasing the sample size decreases the width of the confidence interval. The population from which the sample was drawn is the Forbes 500 Biggest Private Companies. Some preliminary calculations are: §= 2‘ =fl=19427 n . 15 2x2 - (2“? 1,430,756 — (2914): 52 a n _1” = 15 ‘1 15 = 61,761.633 s = 061361.638 = 248.5189 For confidencc coefficient .98, or = 1 Appendix B, with df = 77 — 1 = 1 is: - — .98 = .02 and 011’2 = .020 = .01. From Table VI 5 — 1 -= 14,131 = 2.624. The 98% confidence interva} 9 E 1 {mi a» 194.27 i 2.624% = =194.27 i 1/3 1/? 168.38 ==~ (25.89, 362.65) For confidence coefficient .98. or = l — .98 = .02 and (112 = .0212 = .01. From Table IV Appendix B, em = 2.33. The confidence interval is: p 4; mfg = .144 i 2.33'%@ = .144 i .023 = (.121, .167) We are 98% confident that the proportion of debit cardholders who have used their card in making purchases over the Internet is between .121 and .167. 9 Since we would have less confidence with a 90% confidence interval than with a 98% confidence interval, the 90% interval would be narrower. 5.30 5.34 The point estimate ofp is f: = I101 = 35155 = .636. We must 'check to see if the sample size is sufficiently large: is: 36}, 4.5: 31:22 =.636i #113? =.636i .195=>(.441,.331) Since the interval is wholly contained in the interval (0, 1) We may assume that the normal approximation is reasonable. For confidence coefficient, .99, or = .01 and on? = .0112 = .005. From Table IV, Appendix B, zms = 2.575. The confidence interval is: ,6 i 2305 E‘i = .636 i 2.575 ‘ fig?! = .636 i .167 = (_469, .303) H We are 99% confident that the true proportion of fatal accidents involving children is between .469 and .803. The sample proportion of children killed by air bags who were not wearing seat belts or were improperly restrained is 24135 = .686. This is rather large proportion. Whether a child is kined by an airbag could be related to whether or not hefshe was properly restrained. Thus, the number of children killed by air bags could possibly be reduced if the child were properly restrained. The population studied by Arthur Anderson is the set of all privately~held family firms with revenues exceeding $1,000,000 per year. or the 3,900 observations, 1,911 had no Strategic business plan = f: = 191113.900 = .49. To see if the sample size is sufficiently large: faiaofi=fsis fl=§i3 3:.49i3 49(51) __..—.__ = .49 i .024 n n 3,900 m (.466, .5 14) Since the interval lies within the interval (0, 1), the normal approximation will be adequate. For confidence coefficient .90, o: = .10 and 01/2 = .1012 = .05. From Table IV, Appendix B, 2:05 = 1.645. The confidence interval is: * - p9 * 33:7 .49(.51) + __ w i 1.645 __ a .49 + 1.645 ____ .494; .013 p F 4'05 n p _ n _ 3,900 = = (.471, .503) We are 90% confident that the proportion of family-owned companies without strategic business plans is between .477 and .503. The width of the interval construaed in part b is .503 — .477 = .026. An 80% confidence interval would be narrower because we have less confidence. For confidence coefficient .80, or = .20 and on? = .2012 = .10. From Table IV, Appendix B, 2.10 = 1.28. The confidence interval is: ,5: “01% =4}? 4; 1.281%: = .49 451.2%:9333) =4 .49 i .010 =(.480, .500) The width of the interval constructed in part c is .500 w .480 = .020. This is, in fact, narrower than the 90% confidence interval. \ 5.38 a. To compute the needed sample size, use: (2:112qu n = _.?._ where 22025 = 1.96 from Table IV, Appendix B. 2 Thus, n = (1'96) (2)93) = 96.04 .082 =97 You would need to take a sample of size 97. b. To compute the needed sample size, use: 2 n = M = .(1'96)2('5)('5) = 150 0625 = 151 32 .032 ' You would need to take a sample of size 151. 5.64 a. The point estimate for the fraction of the entire market who refuse to purchase bars is: 23 m , x p:_: n .094 b. To see if the sample size is sufficient: 244 Since the interval above is contained in the interval (0, l), the sample size is sufficiently large. p i flfi a .094 a 3r'0944'906) = .094 i .056 = (.038, .150) c, For confidence coefficient .95, or = 1 — .95 = .05 and 0:12 = .0542 = .025. From Table IV, Appendix B, 2325 = 1.96. The confidence interval is; p i 2025‘??? = .094 i 1.961% a .094 i .037 = (.057, .131) d. The best estimate of the true fraction of the entire market who refuse to purchase bars six months after the poisoning is .094. We are 95% confident the true fracrion of the entire market who refuse to purchase bars six months after the poisoning is between .057 and . 1 3 1. e. For confidence coefficient .95, or = .05 and 0:12 = .025. From Table IV, Appendix B, 2325 = 1.96. From part a, a good approximation for p is .094. Also, B = .02. 2 (7.qu = (l.96)2(.094)(.906) = any a 818 The sample size is n = a2 .022 You would need to take a = 818 samples. 1. . c. 1.96 d. 1.28 5.3 a. 28 :i: .784 b. 102 i .65 c. 15 :1: .0588 d. 4.05 I“ .163 e. no 3”.9 i .65 h. 33.9 i .32 c. width is halved 5.7 (1. claim probablyr not true 5.9 (3526,4921) 5.11 a. 66.83 i 4.69 c. (41.009.49.602) 5.13 a. 2.228 b. 2.228 c. —1.812 d. 1.225 e. 4.032 5.15 a. 97.94 4-1 4.24 b. 97.94 i 6.24 5.17 a. 2.886 :t 4.034 b. .408 I .256 5.19 a. 49.3 I 8.6 h. 99% confident that the mean amonnt removed from all soil specimens using the poison is between 40.70% and 57.90%. 5.21 184.99 :1: 133.93 5.23 a. 22.46 :1: 11.18 :1. validity is suspect 5.25 a. yes b. no c. yes d. no 5.27 a. yes b. .46 i .065 5.29 b. .29 :1: .028 5.31 a. .24 b. .24 :1: .181 5.33 .85 :‘t .002 5.35 308 5.37 a. 68 h. 31 5.39 34 5.41 a. .226 i .00? h. .014 c. 1.680 5.43 1,692 5.45 43; 171; 385 5.47 no 5.49 a. —1.225 b. 3.250 c. 1.860 d. 2.898 5.51 a. 32.5 :t 5.16 13. 23,964 5.53 a. (298.6, 582.3} 5.55 a. .876 .4: .003 5.57 a. men:2.4 i .979; women: 4.5 '1 .755 b. men: 9.3 :1: 1.185; women: 6.6 -|_- 1.138 5.59 a. 12.2 :I: 1.645 b. 167 5.61 a. 191 5.63 b. 3.256 3: .348 5.65 154 5.1 a. El. ...
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This note was uploaded on 09/11/2008 for the course ECON 317 taught by Professor Safarzadeh during the Spring '07 term at USC.

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answer key of chapter 5 - 5.8 a 5.14 For confidence...

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