a. b. a. b. a. a. a. a.

47. a.

95 PI is 20.21, 43.69, no b. 28.53, 51.92, at least 90 49. 431.3, 628.5

51. a.

45 is closer to b. 46.28, 46.78 c. 47.56, 49.84 53. a narrower than b, c narrower than d, a narrower than c, b narrower than d 57. If, for example, 18 is the minimum age of eligibility, then for most people .

59. a.

.966 b. The percent dry fiber weight for the first specimen tends to be larger than for the second. c. No change d. 93.3 e. , so there does appear to be such a relationship.

61. a.

. Using either , yes. b. .560 56, same 63. , yet ; so cannot be rejected.

65. a.

.481 b. , so at level .01, no linear associ- ation. c. At level .01, no positive linear association, but at level .05, there does appear to be positive linear association. t 5 1.98, P-value 5 .07 H : r 5 0 t 5 2.44 , 2.776 r 5 .773 or .01 a 5 .05 r 5 .748, t 5 3.9, P-value 5 .001 t 5 14.9, P-value 0 y x 2 18 x 5 45.18

67. a.

Reject H b. No. , which indicates only a weak relationship. c. Yes, but very large , so no practical significance.

69. a.

95 CI: .888, 1.086 b. 95 CI: 47.730, 49.172 c. 95 PI: 45.378, 51.524 d. Narrower for , since 25 is closer to e. .981

71. a.

, so don’t reject H b. .970

73. a.

.507 b. .712 c. , so reject and conclude that there is a useful linear relationship. d. A 95 CI is 1.056, 1.275. e. 1.0143, .2143

75. a. y

1.69 ⫹ .0805x b. y ⫽ ⫺20.40 ⫹ 12.2254x c. .984

for both regressions.

77. a.

A substantial linear relationship

b. c.

98.3

d. e.

Yes; f. .0394, .0499 g. .762, .858

81. b.

.573 87. , so it is plausible that . b 1 5 g 1 t 5 2 1.14 t 5 19.96 .7702, 2.0902 y 5 2 .08259 1 .044649x H : b 1 5 P -value 5 .0013 , .01 5 a t 5 2 1.24 . 22.201 x x 5 25 n 1 r .022 P -value 5 .00032 1 z 3.6 1 r .16

1. a.

6.32, 8.37, 8.94, 8.37, and 6.32 b. 7.87, 8.49, 8.83, 8.94, and 2.83 c. The deviation is likely to be much smaller for the x values of part b.

3. a.

Yes.

b. ⫺

.31, ⫺.31, .48, 1.23, ⫺1.15, .35, ⫺.10, ⫺ 1.39, .82, ⫺.16, .62, .09, 1.17, ⫺1.50, .96, .02, .65, ⫺2.16, ⫺ .79, 1.74. Here ee ranges between .57 and .65, so e is close to es. c. No.

5. a.

About 98 of observed variation in thickness is explained by the relationship. b. A nonlinear relationship

7. a.

.776 b. Perhaps not, because of curvature. c. Substantial curvature rather than a linear pattern, implying inadequacy of the linear model. A parabola quadratic regression provides a significantly better fit. 9. For set 1, simple linear regression is appropriate. A quad- ratic regression is reasonable for set 2. In set 3, 13, 12.74 appears very inconsistent with the remaining data. The esti- mated slope for set 4 depends largely on the single observa- tion 19, 12.5, and evidence for a linear relationship is not compelling.

11. c.

increases, and decreases. 13. t with ; .02

15. a.

A curved pattern b. A linear pattern

c. d.

A 95 PI is 3.06, 6.50. e. One standardized residual, corresponding to the third observation, is a bit large. There are only two positive standardized residuals, but two others are essentially 0. The patterns in a standardized residual plot and normal probability plot are marginally acceptable.

17. a. c.

, so don’t reject H . d. , so reject H .

19. a.

No b. , where so .

c. d.

using transformed values, , so don’t reject H .

21. a. b.

yˆ 5 15.17 mˆ Y x 5 18.14 2 1485x f 5 .33 , 8.68 5 F .01,1,15 SSE 5 1.39587, SSPE 5 1.36594 aˆ 5 3.70034 10 2 5 , yˆr 5 6.7748, yˆ 5 875.5 bˆ 5 bˆ 1 5 3735.45, bˆ 5 2 10.2045 Y 5 ae b t P Y r 5 ln Y, Y r 5 b 1 b 1 1t 1 Pr H : b 5 1, t 5 24.30 t 5 2 1.07 bˆ 5 1.254 bˆ 5 2 .468, aˆ 5 .626, 18.109, gy i r 2 5 16.572, bˆ 1 5 1.254, gxr i y r i 5 gxr i 5 15.501, gyr i 5 13.352, gxr i 2 5 20.228, Y 5 ax b P n 2 2 df V Y i 2 Yˆ i V Yˆ i Chapter 13 Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook andor eChapters. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.