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268 CHAPTER 7 HYPOTHESIS TESTING
EXERCISES
In each of the following exercises, carry out the ten-step testing procedure. 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
7.7.1 Recall Example 7.2.3, where Nakamura et al. (A-1) studied subjects with acute medial collateral
ligament injury (MCL) with anterior cruciate ligament tear (ACL). The ages of the 17 subjects were:
31, 26, 21, 15, 26, 16, 19, 21, 28, 27, 22, 20, 25, 31, 20, 25, 15
Use these data to determine if there is sufficient evidence for us to conclude that in a population
of similar subjects, the variance of the ages of the subjects is not 20 years. Let a = .01.
7.7.2 Robinson et al. (A-29) studied nine subjects who underwent baffle procedure for transposition of
the great arteries (TGA). At baseline, the systemic vascular resistance (SVR) 1measured in
WU * m 2 2 values at rest yielded a standard deviation of 28. Can we conclude from these data
that the SVR variance of a population of similar subjects with TGA is not 700 Let a = .10.
7.7.3 Vital capacity values were recorded for a sample of 10 patients with severe chronic airway obstruction.
The variance of the 10 observations was .75. Test the null hypothesis that the population
variance is 1.00. Let a = .05.
7.7.4 Hemoglobin (g percent) values were recorded for a sample of 20 children who were part of a study
of acute leukemia. The variance of the observations was 5. Do these data provide sufficient evidence
to indicate that the population variance is greater than 4 Let a = .05.
7.7.5 A sample of 25 administrators of large hospitals participated in a study to investigate the nature and
extent of frustration and emotional tension associated with the job. Each participant was given a test
designed to measure the extent of emotional tension he or she experienced as a result of the duties
and responsibilities associated with the job. The variance of the scores was 30. Can it be concluded
from these data that the population variance is greater than 25 Let a = .05.
7.7.6 In a study in which the subjects were 15 patients suffering from pulmonary sarcoid disease,
blood gas determinations were made. The variance of the PaO 2 (mm Hg) values was 450. Test
the null hypothesis that the population variance is greater than 250. Let a = .05.
7.7.7 Analysis of the amniotic fluid from a simple random sample of 15 pregnant women yielded the
following measurements on total protein (grams per 100 ml) present:
.69, 1.04, .39, .37, .64, .73, .69, 1.04,
.83, 1.00, .19, .61, .42, .20, .79
Do these data provide sufficient evidence to indicate that the population variance is greater than
.05 Let a = .05. What assumptions are necessary
7.8 HYPOTHESIS TESTING: THE RATIO
OF TWO POPULATION VARIANCES
As we have seen, the use of the t distribution in constructing confidence intervals and in
testing hypotheses for the difference between two population means assumes that the
population variances are equal. As a rule, the only hints available about the magnitudes