b)The calculations were based on a volunteer sample rather
than an SRS, so the conclusions should not be taken as describing the
entire population of the city.
15.3 The only source of error included in the stated margin
of error is (c).
15.5
a)(491.4-475)/10 = 1.64 which has a p-value of .0505, so
it is not significant at the .05 level.
b)(491.5-475)/10 = 1.65 which has a p-value of .0495, so it
is significant at the .05 level.
15.6
a)(478-475)/10 = .3 which has a p-value of .3821.
b)(478-475)/3.16 = .95 which has a p-value of .1711.
c)(478-475)/1 = 3 which has a p-value of .0013.
15.7
a)478± 2.576*100/10 = (452.24,503.76)
b)478± 2.576*100/31.6 =(469.85, 486.15)
c)478± 2.576*100/100 = (475.42,480.58)
15.9
a) It is not proper to conclude that the four people have
ESP. With so many tests, it is likely that at least a couple will be
significant just by chance (even at the .01 level).
b) The subjects who did significantly better than random
guessing should be re-tested to see if they score significantly better
than random guessing.
15.10
a) Reject H0 if z< -2.326.
b) Reject H0 if x < 270.18.
c) The probability that x < 270.18
if μ= 270, is approximately .5.
15.13
a) One hypothesis is that patient is in good health. The
other hypothesis is that the patient should see a doctor. A "false
positive" result would have a healthy patient sent to see a doctor
while a "false negative" would send an unhealthy patient home.
15.15
a) 0-0/(1/3) = 0. Probability of rejection H0
when it is true is 0.5.
b) 0 - .3/(1/3) = -.9. Probability of failing to reject
H0 when μ=.3 is .1841
c) 0-1/(1/3) = -3. Probability of failing to reject
H0 (μ=0) when μ=1 is .0013.
15.16 Answers may vary. An example would be any set of
data that includes the whole population would not allow for valid
statistical inference.
15.17 B, A, C
15.20 The estimate is likely to be biased because the
results were based upon responses to questions of a personal and/or
sensitive nature. In these case people sometimes do not tell the truth.
The margin of error does not allow for this bias.
15.21 The 43 Presidents are the population. They are not
a sample. Confidence intervals only make sense in the context of
taking samples from a larger population.
15.22
a) It is risky to regard the shoppers as an SRS because
they were selected at a certain time. Many shoppers (or types of
shoppers) are more likely to be at the store during a particular time
of the week. In other words, not all of the shoppers were equally
likely to have been selected.
b)
0
3 8 9
1
0 2 3 5 5 7 7 8 8 9 9 9
2
0 0 2 3 4 4 5 6 6 7 8 8 8
3
2 4 6 8 9
4
1 2 4 4 5 6 8
5
0 2 4 9
6
1
7
0
8
2 5 6
9
3
The distribution seems to be skewed to the right, so it may not
be a good idea to use the z procedures.
15.23
When many tests are done, it is likely that just by chance some of them
will be significant. A follow-up study should look at those variables
that were found to be significant to see if they do a good job
predicting the outcomes for the newest trainees.