Chapter 11 Solutions
11.1.
Both 283 and 311 pushes per minute are statistics (related to one sample: the subjects
with placebo, and the same subjects with caffeine).
11.2.
41% and 37% are parameters (related to the population of all registered voters in
Florida); 33% is a statistic (related to the sample of registered voters among those called).
11.3.
Both 82% and 18% are statistics, related to those projectile points found at the North
Carolina site. (This assumes that we can view those points as a sample from some
population—either the population of all points buried at that site, or all points buried in
North America.)
11.4.
Sketches will vary; one result is shown on
the right.
11.5.
Although the probability of having to pay for a total loss for 1 or more of the 12 policies
is very small, if this were to happen, it would be financially disastrous. On the other hand,
for thousands of policies, the law of large numbers says that the average claim on many
policies will be close to the mean, so the insurance company can be assured that the
premiums they collect will (almost certainly) cover the claims.
11.6. (a)
The population is the 12,000 students; the population distribution (Normal with mean
7.11 minutes and standard deviation 0.74 minute) describes the time it takes a randomly
selected individual to run a mile.
(b)
The sampling distribution (Normal with mean
7.11 minutes and standard deviation 0.074 minute) describes the average mile-time for 100
randomly selected students.
11.7. (a)
µ
=
694
/
10
=
69
.
4.
(b)
The table on the following page shows the results for
line 116. Note that we need to choose 5 digits, because the digit 4 appears twice. (When
choosing an SRS, no student should be chosen more than once.)
(c)
The results for the other
lines are in the table; the histogram is shown on the right on the following page. (Students
might choose different intervals than those shown here.) The center of the histogram is a bit
lower than 69.4 (it is closer to about 67), but for a small group of
x
-values, we should not
expect the center to be in exactly the right place.
Note:
You might consider having students choose different samples from those prescribed
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Solutions
151
in this exercise, and then pooling the results for the whole class. With more values of
x, a
better picture of the sampling distribution begins to develop.
Line
Digits
Scores
x
116
14459
62 + 72 + 73 + 62 = 269
67.25
117
3816
58 + 74 + 62 + 65 = 259
64.75
118
7319
66 + 58 + 62 + 62 = 248
62
119
95857
62 + 73 + 74 + 66 = 275
68.75
120
3547
58 + 73 + 72 + 66 = 269
67.25
121
7148
66 + 62 + 72 + 74 = 274
68.5
122
1387
62 + 58 + 74 + 66 = 260
65
123
54580
73 + 72 + 74 + 82 = 301
75.25
124
7103
66 + 62 + 82 + 58 = 268
67
125
9674
62 + 65 + 66 + 72 = 265
66.25
60
62
64
66
68
70
72
74
76
78
0
1
2
3
4
Frequency
x-bar value
11.8. (a)
x
is not systematically higher than or lower than
µ
; that is, it has no particular
tendency to underestimate or overestimate
µ
.
(b)
With large samples,
x
is more likely to
be close to
µ
, because with a larger sample comes more information (and therefore less
uncertainty).

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