Introductory Biostatistics

(a) Calculate the 95% confidence interval for the mean systolic blood

pressurechange. Does the oral contraceptive seem to change the

mean systolic blood pressure?

(b)Calculate a 95% confidence interval for Pearson’s correlation coe‰-

cient representing a possible relationship between systolic blood

pressures measured before and after the administration of oral con-

traceptive. What does it mean that these measurements are corre-

lated (if confirmed)?

4.26 Suppose that we are interested in studying patients with systemic cancer
who subsequently develop a brain metastasis; our ultimate goal is to
prolong their lives by controlling the disease. A sample of 23 such
patients, all of whom were treated with radiotherapy, were followed
from the first day of their treatment until recurrence of the original
tumor. Recurrence is defined as the reappearance of a metastasis in
exactly the same site, or in the case of patients whose tumor never com-
pletely disappeared, enlargement of the original lesion. Times to recur-
rence (in weeks) for the 23 patients were: 2, 2, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10,
14, 14, 18, 19, 20, 22, 22, 31, 33, 39, and 195. First, calculate the 95%
confidence interval for the mean time to recurrence on the log scale; then
convert the endpoints toweeks.

4.27 An experimental study was conducted with 136 five-year-old children
in four Quebec schools to investigate the impact of simulation games
designed to teach children to obey certain tra‰c safety rules. The transfer
of learning was measured by observing children’s reactions to a quasi-
real-life model of tra‰c risks. The scores on the transfer of learning for the
control and attitude/behavior simulation game groups are summarized in
Table E4.27. Find and compare the 95% confidence intervals for the
means of the two groups, and draw an appropriate conclusion.

TABLE E4.27

Summarized

Data Control

Simulation

Game

n 30 33

x 7.9 10.1

s 3.7 2.3

4.28 The body mass index is calculated by dividing a person’s weight by the
square of his or her height (it is used as a measure of the extent to which
the person is overweight). A sample of 58 men, selected (retrospectively)
from a large group of middle-aged men who later developed diabetes
mellitus, yieldsx¼ 25 :0 kg/m^2 ands¼ 2 :7 kg/m^2.
(a) Calculate a 95% confidence interval for the mean of this sub-
population.

EXERCISES 183