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202 CHAPTER 6 ESTIMATION
the column headed 3 and the row labeled 15. We now take the reciprocal of this value,
1>4.15 = .24096. In summary, the lower confidence limit (LCL) and upper confidence
limit (UCL) s 2 1>s 2 2 are as follows:
LCL = s 2 1
s 2 2
Alternative procedures for making inferences about the equality of two variances
when the sampled populations are not normally distributed may be found in the book by
Daniel (15).
Some Precautions Similar to the discussion in the previous section of constructing
confidence intervals for s 2 , the assumption of normality of the populations from
which the samples are drawn is crucial to obtaining correct intervals for the ratio of variances
discussed in this section. Fortunately, most statistical computer programs provide
alternatives to the F-ratio, such as Levene’s test, when the underlying distributions cannot
be assumed to be normally distributed. Computationally, Levene’s test uses a measure
of distance from a sample median instead of a sample mean, hence removing the
assumption of normality.
1
F 11-a>22,df1 ,df 2
UCL = s 2 1
s 2 F 1-1a>22, df2 ,df 1
2
EXERCISES
6.10.1 The purpose of a study by Moneim et al. (A-26) was to examine thumb amputations from team
roping at rodeos. The researchers reviewed 16 cases of thumb amputations. Of these, 11 were complete
amputations while five were incomplete. The ischemia time is the length of time that insufficient
oxygen is supplied to the amputated thumb. The ischemia times (hours) for 11 subjects
experiencing complete amputations were
4.67, 10.5, 2.0, 3.18, 4.00, 3.5, 3.33, 5.32, 2.0, 4.25, 6.0
For five victims of incomplete thumb amputation, the ischemia times were
3.0, 10.25, 1.5, 5.22, 5.0
Treat the two reported sets of data as sample data from the two populations as described.
Construct a 95 percent confidence interval for the ratio of the two unknown population
variances.
6.10.2 The objective of a study by Horesh et al. (A-27) was to explore the hypothesis that some forms
of suicidal behavior among adolescents are related to anger and impulsivity. The sample consisted
of 65 adolescents admitted to a university-affiliated adolescent psychiatric unit. The researchers
used the Impulsiveness-Control Scale (ICS, A-28) where higher numbers indicate higher degrees
of impulsiveness and scores can range from 0 to 45. The 33 subjects classified as suicidal had an
ICS score standard deviation of 8.4 while the 32 nonsuicidal subjects had a standard deviation of
6.0. Assume that these two groups constitute independent simple random samples from two