Chapter 7
1. a.
99.5
b.
85
c.
2.96
d.
1.15
3. a.
Narrower
b.
No
c.
No
d.
No
5. a.
4.52, 5.18
b.
4.12, 5.00
c.
.55
d.
94
7.
By a factor of 4; the width is decreased by a factor of 5.
9. a.
; 4.57, `
b. c.
;
11.
950, .8714
13. a.
608.58, 699.74
b.
189
15. a.
80
b.
98
c.
75
17.
134.53
19.
.513, .615
21.
with 95 confidence; yes
23. a.
with 95 confidence.
b.
If the same formula is used on sample after sample, in the long run the actual value of p will exceed about 95 of
the calculated lower bounds.
25. a.
381
b.
339
29. a.
2.228
b.
2.086
c.
2.845
d.
2.680
e.
2.485
f.
2.571
31. a.
1.812
b.
1.753
c.
2.602
d.
3.747
e.
2.1716 from Minitab
f.
Roughly 2.43
33. a.
Reasonable amount of symmetry, no outliers
b.
Yes based on a normal probability plot
c.
430.5, 446.1, yes, no p .
.044 p ,
.273 2`, 59.7
2`, x 1 z
a
s 1n
x 2 z
a
s 1n, `
x 2 1.645s 1n, `
35. a.
95 CI: 23.1, 26.9
b.
95 PI: 17.2, 32.8, roughly 4 times as wide
37. a.
.888, .964
b.
.752, 1.100
c.
.634, 1.218
39. a.
Yes
b.
6.45, 98.01
c.
18.63, 85.83
41.
All 70; c, because it is shortest
43. a.
18.307
b.
3.940
c.
.95
d.
.10
45.
3.6, 8.1; no
47. a.
95 CI: 6.702, 9.456
b.
.166, .410
49. a.
There appears to be a slight positive skew in the middle half of the sample, but the lower whisker is much longer
than the upper whisker. The extent of variability is rather substantial, although there are no outliers.
b.
Yes. The pattern of points in a normal probability plot is reasonably linear.
c.
33.53, 43.79
51. a.
.539, .581
b.
2398
c.
No—97.5
53. 55.
246
57. 59. a.
b. c.
b; 4.2, 7.65
61.
73.6, 78.8 versus 75.1, 79.6 max x
i
, max x
i
a
1n
max x
i
1 2 a2
1n
, max x
i
a2
1n
2t
r
x
12a2, 2r 2
, 2t
r
x
2 a
2, 2r
5 65.3, 232.5 2.84, 2.16
Chapter 8
1. a.
Yes
b.
No
c.
No
d.
Yes
e.
No
f.
Yes
5.
versus . I: conclude variability in
thickness is satisfactory when it isn’t. II: conclude variabil- ity in thickness isn’t satisfactory when in fact it is.
7.
I: concluding that the plant isn’t in compliance when it is; II: concluding that the plant is in compliance when it isn’t.
9. a. R
1
b.
I: judging that one of the two companies is favored over the other when that is not the case; II: judg-
ing that neither company is favored over the other when in fact one of the two really is preferred.
c.
.044
d. e.
Reject H in favor of H
a
.
11. a.
versus
b.
.01
c.
.5319, .0078
d.
2.58 H
a
: m 2 10 H
: m 5 10 b
.3 5 b.7 5 .488, b.4 5 b.6 5 .845 H
a
: s , 0.5 H
: s 5 0.5
e.
10.1032 is replaced by 10.124, and 9.8968 is replaced by 9.876.
f.
, so H should not be rejected.
g. 13. b.
.0004, 0, less than .01
15. a.
.0301
b.
.003
c.
.004
17. a.
, so reject H .
b.
.8413
c.
143
d.
.0052
19. a.
, so don’t reject H .
b.
.2266
c.
22
21. a.
, so don’t reject .
b.
, so don’t reject H .
c.
Don’t reject H .
d.
Reject H in favor of
.
23.
, so H should be rejected. The data does
suggest a contradiction of prior belief. t 5
2.24 1.708 H
a
: m 2 .5 2
1.6 . 22.179 H
: m 5 .5 t
.025,12
5 2.179 . 1.6
z 5 2 2.27
z 5 2.56 2.33
z 2.58 or 22.58
x 5 10.020
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