text
stringlengths
0
6.73k
Xyn
37. a..9615 b..0617 bs bat
39. a. Sinn + D4 b..25, n(n + 1)Qn + 1/24 19876 be GOS
41, 10:52.74 15. a. 0=SDX2/(2n) b. 74.505
43. AB, 17. b.4/9
45. b. My) = ML — F/2n)} 19. a. p=21—.30=.20 .p = (1002 —9)/70
47. Because 7; is the sum of v independent random variables, 31. a.15 byes. .4437
each distributed as 7, the Central Limit Theorem applies. .
23, a. 0 = (2 1)/(1-3) =3
53. 2.3.2. 10.04, the square of the answer to (a) b. = [-n/Zin(x)] —1= 3.12
ST: Dalla 2)s ae 2 3 25. p=r/(r+x)=.15 This is the number of successes
b. 2v3(v1 + v2 —2)/[vi(v2 — 2)°(v2 —4)}, v2 > 4 over the number of trials, the same as the result in
61. 0.432 Exercise 21, It is not the same as the estimate of
Exercise 17.
65. a. The approximate value, .0228, is smaller because of 50. RASA. dl HC
skewness in the chi-squared distribution 2a =, OX be = 5 UX?
b. This approximation gives the answer 03237, agreeing 9g, ) — 5~x2/(2n) — 74.505, the same as in Exercise 15
with the software answer to this number of decimals. ‘
Ea
67. No, the sum of the percentiles is not the same as the b. 4 20In(2) = 10.16
percentile of the sum, except that they are the same for 34, j= — In(p)/24 = .0120
the 50th percentile. For all other percentiles, the
percentile of the sum is closer to the SOth percentile 33. No, statistician A does not have more information,
than is the sum of the percentiles
69. a. 2360, 73.70 b..9713
37. WS max(x1, X2, Xn) SO < min@r, x2, ..-n))
71. 9685
39. a. 2X(n — X/[n(n — 1)
73. 9093 Independence is questionable because con- was ~
sumption one day might be related to consumption the 41. a Xb. (XK —e)/V1— 1/n)
next day.
--- Trang 837 ---
824 Chapter 8
43. a.V(0)=P/[n(n+2)] db. Pn 33. a. (38.081, 38.439) —_b, (100.55, 101.19), yes
¢. The variance in (a) is below the bound of (b), but the | _
theorem does not apply because the domain is a 35+ @ Assuming normality, a 95% lower confidence bound
finclionét tie'parsmeter is 8.11. When the bound is calculated from repeated
independent samples, roughly 95% of such bounds
45. a. Xb. Nu, o7/n) should be below the population mean,
c. Yes, the variance is equal to the Cramér-Rao bound b. A 95% lower prediction bound is 7.03. When the
d. The answer in (b) shows that the asymptotic bound is calculated from repeated independent
distribution of the theorem is actually exact here. samples, roughly 95% of such bounds should be
‘ below the value of an independent observation,
47. a. 2a”
b. The answer in (a) is different from the answer, 37. a.378.85 b.413.09 _e. (333.88, 407.50)
1/(20*), to 46(a), so the information does depend on
dive paratneteriestioti, 39, 95% prediction interval: (.0498, .0772)
49, 1 = 6/ (616 — ty —...~ ts) = 6/(01 +202 +... + 6x6) = 0436, 41+ B+ (169.36, 179.37)
Wie Sheek hn Beeb b. (134.30, 214.43), which includes 152
¢. The second interval is much wider, because it allows
53. 1.275, s = 1.462 for the variability of a single observation.
6 . d. The normal probability plot gives no reason to doubt
55. b. no, E(a*) = 07/2, so 26° is unbiased normality. This is especially important for part (b), but
59, 416, 448 the large sample size implies that normality is not so
critical for (a).
61. d(X) = (—1)*, 6(200) = 1, 6199) = -1
45. 2.18307 b.3.940 95d. .10
63. b. B =X xiy;/3D17 = 30.040, the estimated minutes
per item; a =F S(yi — pri)? = 16.912; 7s 34, 5:60),
258.= 751 49. a. (7.91, 12.00)
b. Because of an outlier, normality is questionable for
this data set.
Chapter 8 ¢. In MINITAB, put the data in Cl and execute the
following macro 999 times
1. 299.5% b.85% 6.297 9 dL LIS Let k3 =N(c1)
sample k3clc3;
3. a. Anarrower interval has a lower probability _b. No, replace,
Ass not random let k1 =mean(c3)
¢. No, the interval refers to 1, not individual observations giecme cscs
d. No, a probability of 95 does not guarantee 95 aha
successes in 100 trials
51. a. (26.61, 32.94)
3 52218) G28) eS de b. Because of outliers, the weight gains do not seem
7. Increase n by a factor of 4. Decrease the width by a factor normally distributed.
of 5. ¢. In MINITAB, see Exercise 49(c).
9. a. (¥— 1.6450/ fi, 00); (4.57, 00) 53.2. G8.46, 38.84)
b. G22 0/V/n,00) b. Although the normal probability plot is not perfectly
a: straight, there is not enough deviation to reject
c. (=00,8 + 24+ @/ Vi); (—90, 59.7) normality.
11. 950; .8724 (normal approximation), .8731 (binomial) ¢ In MINITAB, see Exercise 49(c).
13. a. (.99, 1.07) b. 158 SBuri ass LOTS, 205345)
b. Because of an outlier, normality is questionable for
15. a. 80% — b.98% —€. 75% this data set.
¢. In MINITAB, see Exercise 49(c).
17. .06, which is positive, suggesting that the population
mean change is positive 57. a. In MINITAB, put the data in Cl and execute the
following macro 999 times
19. (513, .615) Tet k3 oN(61)
21. 218 sample k3cl¢3;
replace.
23. (.439, .814) let k1 = stdev(c3)
stackklc5c5
25. a.381 —b.339 end
29, 01341 b.1.753. 1.708. 1.684 b. Assuming normality, a 95% confidence interval for
©2704 cis (3.541, 6.578), but the interval is inappropriate
because the normality assumption is clearly not
31. a.2.228 2131 2.947 4.604 satisfied.
e.2.492 £.2.715