dence? (Use a conservative estimate because no prior estimate of
the prevalence in this city is assumed available.)
(b)A similar study was recently conducted in another state. Of the
13,573 blacks sampled, 1085 were found to have sickle cell anemia.
Using this information, resolve part (a).12.14 A researcher wants to estimate the average weight loss obtained by
patients at a residential weight-loss clinic during the first week of a
controlled diet and exercise regimen. How large a sample is needed to
estimate this mean to within 0.5 lb with 95% confidence? Assume that
past data indicate a standard deviation of about 1 lb.
12.15 Suppose that a study is designed to select the better of two treatments.
The endpoint is measured on a continuous scale and a treatment is said
to be better if the true mean is 10 units larger than the mean associated
with the other treatment. Suppose also that the two groups have the
same variance, which is estimated at abouts^2 ¼400. Find the total
sample size needed if we want 99% certainty of making the right selec-
tion.
12.16 Suppose that in planning for a phase II trial, an investigator believes
that the incidence of severe side e¤ects is about 5% and the trial has to
be stopped if the incidence of severe side e¤ects exceeds 20%. Preset the
level of significance at 0.05 and design a stopping rule that has a power
of 90%.
12.17 A study will be conducted to determine if some literature on smoking
will improve patient comprehension. All subjects will be administered a
pretest, then randomized into two groups: without or with a booklet.
After a week, all subjects will be administered a second test. The data
(di¤erences between prescore and postscore) for a pilot study without a
booklet yielded (score are on a scale from 0 to 5 points)
n¼ 44 ; x¼ 0 : 25 ; s¼ 2 : 28How large should the total sample size be if we decide to preset
a¼ 0 :05 and that it is important to detect a mean di¤erence of 1.0 with
a power of 90%?12.18 A study will be conducted to investigate a claim that oat bran will
reduce serum cholesterol in men with high cholesterol levels. Subjects
will be randomized to diets that include either oat bran or cornflakes
cereals. After two weeks, LDL cholesterol level (in mmol/L) will be
measured and the two groups will be compared via a two-samplettest.
A pilot study with cornflakes yields
n¼ 14 ; x¼ 4 : 44 ; s¼ 0 : 97478 STUDY DESIGNS