Biostatistics

EXERCISES 271
EXERCISES
In the following exercises perform the ten-step test. For each exercise, as appropriate, explain why
you chose a one-sided test or a two-sided test. Discuss how you think researchers or clinicians might
use the results of your hypothesis test. What clinical or research decisions or actions do you think
would be appropriate in light of the results of your test?
7.8.1 Dora et al. (A-31) investigated spinal canal dimensions in 30 subjects symptomatic with disc
herniation selected for a discectomy and 45 asymptomatic individuals. The researchers wanted to
know if spinal canal dimensions are a significant risk factor for the development of sciatica. Toward
that end, they measured the spinal canal dimension between vertebrae L3 and L4 and obtained a
mean of 17.8 mm in the discectomy group with a standard deviation of 3.1. In the control group, the
mean was 18.5 mm with a standard deviation of 2.8 mm. Is there sufficient evidence to indicate that in
relevant populations the variance for subjects symptomatic with disc herniation is larger than the
variance for control subjects? Let a ¼ :05.
7.8.2 Nagy et al. (A-32) studied 50 stable patients who were admitted for a gunshot wound that traversed
the mediastinum. Of these, eight were deemed to have a mediastinal injury and 42 did not. The
standard deviation for the ages of the eight subjects with mediastinal injury was 4.7 years, and the
standard deviation of ages for the 42 without injury was 11.6 years. Can we conclude from these data
that the variance of age is larger for a population of similar subjects without injury compared to a
population with mediastinal injury? Let a ¼ :05.
7.8.3 A test designed to measure level of anxiety was administered to a sample of male and a sample of
female patients just prior to undergoing the same surgical procedure. The sample sizes and the
variances computed from the scores were as follows:
Males: n ¼ 16; s 2 ¼ 150
Females: n ¼ 21; s 2 ¼ 275
Do these data provide sufficient evidence to indicate that in the represented populations the scores
made by females are more variable than those made by males? Let a ¼ :05.
7.8.4 In an experiment to assess the effects on rats of exposure to cigarette smoke, 11 animals were
exposed and 11 control animals were not exposed to smoke from unfiltered cigarettes. At the end
of the experiment, measurements were made of the frequency of the ciliary beat (beats/min at
20 C) in each animal. The variance for the exposed group was 3400 and 1200 for the unexposed
group. Do these data indicate that in the populations represented the variances are different?
Let a ¼ :05.
7.8.5 Two pain-relieving drugs were compared for effectiveness on the basis of length of time elapsing
between administration of the drug and cessation of pain. Thirteen patients received drug 1, and 13
received drug 2. The sample variances were s 2 1 ¼ 64 and s2 2 ¼ 16. Test the null hypothesis that the two
populations variances are equal. Let a ¼ :05.
7.8.6 Packed cell volume determinations were made on two groups of children with cyanotic congenital
heart disease. The sample sizes and variances were as follows:
Group n s 2
1 10 40
2 16 84