Ch12

The Practice of Statistics: TI-83/89 Graphing Calculator Enhanced

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Inference for Proportions 12.1 (a) Population: the 175 residents of Tonya's dorm; p is the proportion who like the food. (b) j? = 0.28. 12.2 (a) The population is the 2400 students at Glen's college, and p is the proportion who believe tuition is too high. (b) fi = 0.76. 12.3 (a) The population is the 15,000 alumni, and #I is the proportion who support the president's decision. (b) b = 0.38. 12.4 (a) No-the population is not large enough relative to the sample. (b) Yes-we have an SRS, the population is 48 times as large as the sample, and the success count (38) and failure count (12) i are both greater than 10. (c) No-there were only 5 or 6 "successes" in the sample. 12.5 (a) No-np, and n(l - 0,) are less than 10 (they both equal 5). (b) No-the expected number of failures is less than 10 (n(1 - p,) = 2). (c) Yes-we have an SRS, the population is more than 10 times as large as the sample, and np, = n(l - = 10. 12.6 (a) SEb = d(0.54)(0.46)/1019 = 0.01561, so the 95 % confidence interval is 0.54 r (1.96)(0.01561) = 0.51 to 0.57. The margin of error is about 3%, as stated. (b) We weren't given sample sizes for each gender. (However, students who know enough algebra can get a good estimate of those numbers by solving the system x + y = 1019 and 0.65~ + 0.43~ = 550: approximately 508 men and 511 women.) (c) The margin of error for women alone would be greater than 0.03 since the sample size is smaller. 12.7 (a) The methods can be used here, since we assume we have an SRS from a large population, and all relevant counts are more than 10. For TVs in rooms: b1 2 0.66 and SE5 = d(0.66)(0.34)/1048 = 0.01463, so the 95% confidence interval is 0.66 ? (1.96)(0.01463) = 0.631 to 0.689. For preferring Fox: bi = 0.18 and SE4 = d(0.18)(0.82)/1048 = 0.01187, so the 95% confidence interval is 0.18 5 (1.96)(0.01187) = 0.157 to 0.203. (b) In both cases, the margin of error for a 95% confidence interval ("19 cases out of 20") was (no more than) 3 % . (c) We test H,: p = 0.5 versus Ha: p > 0.5. The test statistic is z = (0.66-0.50)/- 10.36, which gives very strong evidence against H, (P < 0.0002); we conclude that more than half of teenagers have TVs in their rooms. (Additionally, the interval from (a) does not include i 0.50 or less.) With the TI-83, z = 10.379 and P = 1.577 x 12.8 (a) = .66, and since 4 = 132 and n(1 - b) = 68 are both greater than 10, the confidence interval based on z can be used. The 95% confidence interval for p is .66 ? (1.96)V'((.66)(.34)/200) = .66 ? 0.06565, or 0.59435 to 0.72565.
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Chapter 12 i/ (b) Yes; the 95% confidence interval contains only values that are less than 0.73, so it is likely that for this particular population, p differs from 0.73 (specifically, is less than 0.73). 12.9 (a) fi = 8 = 0.1786, and SEg = db(1 - b)/84 = 0.0418. (b) Checking conditions, 4 = 15 and n(l - fi) = 69 are both at least 10. Provided that there are at least (84) (P) = 840 applicants in the population of interest, we are safe constructing the confidence inerval. b + 1.645 SEg = 0.1098 to 0.2473. 1645 2 12.10 n = (m) (0.7)(0.3) = 355.2-use n = 356. With = 0.5, SEb = 0.0265, so the true mar- gin of error is (1.645)(0.0265) = 0.0436. 12.1 1 (a) 105 1.7-round up to 1052. (b) 1067.1-round up to 1068; 16 additional people. 12.13 (a) We do not know that the examined records came from an SRS, so we must be cautious in drawing emphatic conclusions. Both 4, n(l - b) are at least 10. b = = 0.3168; SEb = dfi(1 - fi)/1711 = 0.01 125; the interval is 5 1.960 SEp = 0.2947 to 0.3388. (b) No: We do not know; for example, what percentage of cyclists who were not involved in fatal accidents had alcohol in their systems.
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Ch12 - Inference for Proportions 12.1 (a) Population: the...

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