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 Solutions
to Practice Problems
1) Since the patients do not represent a random sample from any
population, it is not possible to make any inference about this result
holding for a larger population. Since the study was observational, with
subjects not randomly assigned to treatments, no causal inference can be
made. We just know that for these patients, those who take vitamin C
have
fewer canker sores than those who don't. We don't know why, and we don't
know if this result would be consistent with another group.
2) Since the patients do not represent a random sample from any
population, it is not possible to make any inference that this result
would
hold for a larger population. However, the treatments were randomly
assigned
to the subjects, so (assuming other factors were controlled or
randomized)
the difference in proportions having canker sores can be attributed to
the
vitamin C. We don't know if this result would be consistent with another
group, but we believe we know why, for this group, the proportions
differ.
3) Since the patients selected were a random sample of dental patients
in town, we can infer that the results observed in this experiment
would be
consistent with results from the whole population of dental patients in
this
town. However, since the study was observational, with subjects not
being
randomly assigned to treatments, no causal inference can be made. We
believe
that for the population of dental patients in this town, that those
taking
vitamin C have fewer canker sores than those who didn't. We don't know
if it
is the vitamin C that causes this reduction or some other confounding
variable. We cannot conclude that for the general population, those
taking
vitamin C have fewer canker sores, since the sample was only of dental
patients. To the extent that the dental patients in this town are
representative of dental patients in general, we can infer that dental
patients who take vitamin C tend to have fewer canker sores than those
who
don't.
4) Since the patients selected were a random sample of dental patients
in town, we can infer than the results observed in this experiment
would be
consistent with results from the whole population of dental patients in
this
town. Moreover, the treatments were randomly assigned to the subjects,
so
(assuming other factors were controlled or randomized) the difference in
proportions having canker sores can be attributed to the vitamin C. We
believe that for the population of dental patients in this town, that
those
taking vitamin C have fewer canker sores than those who don't. Also, we
believe that the reduction in canker sores is a consequence of taking
the
vitamin C. We cannot conclude that for the general population, those
taking
vitamin C have fewer canker sores, since the sample was only of dental
patients. To the extent that the dental patients in this town are
representative of dental patients in general, we can infer that dental
patients who take vitamin C tend to have fewer canker sores than those
who
don't, as a result of taking the vitamin C.
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