REFERENCES 937.8 In an experiment reported in the Lancet on the effectiveness of isoniazid as
a treatment for leprosy in rats, the log survival times (weeks) were evaluated.
For untreated rats, the log times were 1.40, 1.46, 1.48, 1.52, 1.53, 1.53, 1.56,
1.58, 1.62, and 1.65. For treated rats, they were 1.71, 1.72, 1.83, 1.85, 1.85,
1.86, 1.86, 1.90, 1.92, and 1.95. The rats were randomly assigned to the two
groups, so the groups are independent. If log times in the untreated group are
called X1 and in the treated group are called Xz, the sample means and sums
of squares of deviations are 511 = 1.533, x2 = 1.845, XI -511)~ = .050,
and C(X2 - x2)2 = ,054. Calculate (a) sp; (b) the degrees of freedom; and
(c) a 99% confidence interval for the true mean difference in log units: (d) On
the basis of the interval obtained in (c), do you feel reasonably sure that the
treatment was effective? Why?
7.9 Bacterial colonies were counted on 12 plates. There were two observers, and
the plate counts obtained were as follows:
Plate Number Observer 1 Observer 2 Difference
1 139 191 -52
2 121 181 - 60
3 49 67 -18
4 163 143 20
5 191 234 -43
6 61 80 - 19
7 179 250 -7 1
8 218 239 -21
9 297 289 8
10 165 20 1 -36
11 91 80 11.
12 92 99 -7
Give a 99% confidence interval for the difference between the mean plate counts
of the two observers. Do you believe that there is a difference? Why?7.10 A physician is planning to take systolic blood pressure measurements from a
group of office workers and a group of repair personnel working for a telephone
company. Past results indicated that c is approximately 15 mmHg. If it is
desired to have a 95% confidence interval of length 4 mmHg, how many workers
should be measured in each group?
REFERENCESvanBelle, G., Fisher, L. D., Heagerty, P. J. and Lumley, T. [2004]. Biostutistics: AMethodology
for the Health Sciences, 2nd ed., Hoboken, NJ: Wiley-Interscience, 86-87, 93-95.
Rothman, K. J. [1986]. Modern Epidemiology, Boston, MA: Little, Brown, 119-125.