Chapter 6

6.1-2: (a) 15/256; (b) 1/32
6.1-4: (a) 0.036

6.2-6: 

6.3-4: (a) 0.05; (b) 0.9916; (c) 0.0122

(b) 0.879
6.3-14: (a) x-bar: 24.5 and 1.805; y-bar: 21.3 and 0.911; N(3.2, 2.716); (c) 0.9738

6.4-6: (a) 2/3 and 2/9; (b) 0.4332

6.5-2: (a) 0.855; (b) 0.8543
6.5-14: (a) 0.2417; (b) 0.220; (c) 0.2244

7.1-4: (a) 56.2857; 56.2062; (b) 56.2857; (c) Yes; (d) The sample mean is better because its variance is 56.2857/98 = 0.5743, compared the the variance of the sample variance, which is 65.8956.
7.1-12: (d) c = 1/(n-1)

7.2-2: (a) [77.272, 92.728]; (b) [79.12, 90.88]; (c) [80.065, 89.935]; (d) [81.154, 88.846]

7.3-4: (a) 393.314; (b) [179.148, 607.48]
7.3-6: (a) [-115.48, 129.105]; (b)

(c) No.

7.4-4: (a) [0.119, 0.684]; (b) [0.345, 0.827]; (c) [0.320, 0.772]

7.5-12: (a) 0.551, 0.793; (b) [-0.305, -0.179]

7.6-8: Using p = 0.08, n = 453
7.6-16: (a) 430; (b)578; (c) 587

7.7-6: (a) (21.0, 21.3); (b) (21.4, 21.6); (c) (21.6, 21.8)

7.8-1: (a)

(b)Estimated final = 11.13 + 1.016(midterm); (c) 22.5.
7.8-5: (a) -0.82; Estimated "0-60" = 10.61 - 0.015(HP);
(b)
(c) r = 0.1486; Estimated "0-60" = 5.47 + 0.0004(weight); (e) HP
7.8-9: [-29.04, 51.31]; [0.478, 1.553]; [10.26, 82.57]
7.8.11: (a) estimated total weight = 15.7 + 0.62(number of pieces);
(b)

(c) 0.2883; (d) [.442, .798]

7.9-1: (a) (75.28278, 85.11336); (83.83844, 90.77724); (89.10713, 99.72809)
          (b) (68.20615, 92.18999); (75.83253, 98.78315); (82.25837, 106.57685)
7.9-4: (a) (51.29439, 52.01561); (48.81439, 49.53561); (50.20680, 50.62320)
          (b) (50.65652, 52.65348); (48.17652, 50.17348); (49.46092, 51.36908)

8.1-4: (a) 0.1538
(b) 0.1538
8.1-6: (a) z < -1.645
(b) z = -2.05, reject Ho at alpha = 0.05. There is statistical evidence that p < 1/6.
(c) 0 < p < 0.1648 : No, p = 1/6 is not in this interval.
8.1-12: (a) z > 1.96
(b) z = 2.054, reject Ho at alpha =  0.025.
(c) p-value = 0.02 < 0.025, so reject Ho at alpha = 0.025. There is statistical evidence that p > 0.65.
(d) 0.659 < p < 1; Reject Ho at alpha = 0.05 since p = 0.65 is not included in the interval. Again, there is statistical evidence that p > 0.65.
8.1-18: (a) The test is to reject Ho if |z| > 1.96. Since z = 8.99, reject Ho at alpha = 0.05. There is statistical evidence that Ha is true.
(b) [0.30, 0.44]. Since this interval does not include 0, we have statistical evidence at alpha = 0.05 that Ha is true.
(c) [0.455, 0.525].

8.2-2: (a) Reject Ho since t(obs) = 3.0 > 1.753.
(b) p-value = 0.0045
8.2-8: (a) Reject Ho if t > 2.764
(b) t = 0.699, so do not reject Ho. There is not statistical evidence at alpha = 0.01 that the mean weight of all home born babies is greater than 3315.
(c) p-value = 0.25
(d) Reject Ho if chi-squared < 3.940.
(e) Chi-squared = 4.104, therefore do not reject Ho. There is not statistical evidence at alpha = 0.05 that the variance of the weights of all home born babies is less than (525)^2.
(f) 0.05 < p-value < 0.10.

8.3-16: (a) Reject if Z > 1.96
(b) Z = 8.98, reject Ho at significance level 0.05.
(c) yes, it appears that both the mean and variance of Y are larger.

8.4-2: Q = 3.784, p-value > 0.10. Ho is not rejected for any reasonable significance level.
8.4-14: Q = 4.44, p-value > 0.10. Ho is not rejected.

8.9-1: Exact method - T = 21, p-value = 0.047 (Note that the approximate p-value is too small, but the same conclusion will result).
8.9-2: Exact method - T = 84, p-value = 0.0604. Moderate evidence to reject Ho.
Normal approximation - w = 132, p-value = 0.0613.
8.9-3: (b) Exact method - T = 77, p-value = 0.0101.
8.9-5: Exact method - T = 33, p-value = 0.0677.
8.9-7: Exact method - T = 19.5, p-value = 0.0176.
8.9-9: Exact method - T = 65, p-value < 0.01.
8.9-11: Exact method - T = 95, p-value > 0.20.