Chapter 12
1. a.
The accompanying displays are based on repeating each stem value five times once for leaves 0 and 1, a second time
for leaves 2 and 3, etc.. 17
17 2 3
17 4 4 5
17 6 7
17 stem: hundreds and tens
18 0 0 0 0 0 1 1
leaf: ones 18
2 2 2 2 18
4 4 5 18
6 18
8 There are no outliers, no significant gaps, and the distri-
bution is roughly bell-shaped with a reasonably high degree of concentration about its center at approxi-
mately 180.
8 8 9 1
0 0 0 0 1
3 1
4 4 4 4 1
6 6 1
8 8 8 9 stem: ones
2 1 1 leaf:
tenths 2
2 5
2 6
2 3
0 0 A typical value is about 1.6, and there is a reasonable
amount of dispersion about this value. The distribution is somewhat skewed toward large values, the two largest of
which may be candidates for outliers. b.
No, because observations with identical x values have different y values.
c.
No, because the points don’t appear to fall at all close to a line or simple curve.
3.
Yes. Yes.
5. b.
Yes.
c.
There appears to be an approximate quadratic relation- ship points fall close to a parabola.
7. a.
5050
b.
1.3
c.
130
d. 9. a.
.095
b. c.
.830, 1.305
d.
.4207, .3446
e.
.0036
11. a. b.
3.00, 2.50
c.
.3627
d.
.4641
13. a.
Yes, because .
r
2
5 .972
2 .01, 2.10
2 .475
2 130
15. a.
2 9
3 3 3 5 5 6 6 6 7 7 8 8 9
4 1 2 2 3 5 6 6 8 9
5 1
6 2 9
7 9
8 Typical value in low 40s, reasonable amount of variability,
positive skewness, two potential outliers b.
No
c.
. No; danger of extrapolation
d.
18.736, 71.605, .738, yes
17. a.
; yes.
b.
We estimate that the expected decrease in porosity associated with a 1-pcf
increase in unit weight is .905.
c.
Negative prediction, but y can’t be negative.
d. e.
.938, roughly the size of a typical deviation from the estimated
regression line.
f.
.974
19. a. b.
339.51
c. d.
The ’s are 125.6, 168.4, 168.4, 211.1, 211.1, 296.7, 296.7, 382.3, 382.3, 467.9, 467.9, 553.4,
639.0, 639.0; a 45° line through 0, 0.
21. a.
Yes;
b.
368.89
c.
368.89
23. a.
16,213.64; 16,205.45
b.
414,235.71; yes, since .
27.
29. Data set r
2
s
Most effective: set 3 1
.43 4.03
Least effective: set 1 2
.99 4.03
3 .99
1.90
31. a.
.893
b.
.01837
c. 33. a.
.081, .133
b.
, no
35. a.
.63, 2.44 is a 95 CI.
b.
Yes.
c.
No; extrapolation
d.
.54, 2.82, no
37. a.
Yes. . Note:
There is one mild out- lier, so the resulting normal probability plot is not entirely
satisfactory. b.
Yes. , so reject
in favor of
39. 43.
, and .
45. a.
77.80, 78.38
b.
76.90, 79.28, same center but wider
c.
wider, since 115 is further from
d. t 5 2
11, P-value 5 0 x
b .1
d 5 1.20, df 5 13
f 5 71.97, s
bˆ
1
5 .004837, t 5 8.48, P-value 5 .000
H
a
: b
1
, 1
H : b
1
5 1
t 5 2 5.8, P-value 0
t 5 7.99, P-value 0
t 3.6, P-value .004
H
a
: b
1
. .1, P-value 5 .277
2.216, 2.136 bˆ
1
5 ⌺x
i
Y
i
⌺x
i 2
r
2
5 .961
r
2
5 .985
yˆ
i
2 85.57
y 5 2 45.5519 1 1.7114x
2 .52, .49
118.91 2 .905x y 5
3.2925 1 .10748x 5 7.59
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