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Chapter 3: Q. 3.153 (page 136)
Regarding the interquartile range,
(a) What type of descriptive nature is it?
(b) What does it measure?
(a) The interquartile range is the difference between the first quartile and third quartile.
(b) The interquartile range is a measure of variability.
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Although, in practice, sample data are generally analyzed in inferential studies, what is ultimate objectives of such studies ?
Sickle Cell Disease. A study published by E. Anionwu et al. in the British Medical Journal (Vol. , pp. ) examined the steady-state hemoglobin levels of patients with three different types of sickle cell disease: HB SC. HB SS. and HB ST. Use the following boxplots to compare the hemoglobin levels for the three groups of patients, paying special attention to center and variation.
Copperhead and Tiger Snakes. S. Fearn et al. compare two types of snakes in the article 鈥淏ody Size and Trophic Divergence of Two Large Sympatric Elapic Snakes in Tasmania鈥� (Australian Journal of Zoology, Vol. 60, No. 3, pp. 159-165). Tiger snakes and lowland copperheads are both large snakes confined to the cooler parts of Tasmania. The weights of the male lowland copperhead in Tasmania have a mean of 812.07 g and a standard deviation of 330.24 g; the weights of the male tiger snake in Tasmania have a mean of 743.65 g and a standard deviation of 336.36 g.
a. Determine the z-scores for both a male lowland copperhead snake and a male tiger snake whose weights are 850 g.
b. Under what conditions would it be reasonable to use z-scores to compare the relative standings of the weights of the two snakes?
c. Assuming that a comparison using z-scores is legitimate, relative to the other snakes of its type, which snake is heavier?
Each of the following smooth curves represents the shape of a data set. In each case, decide whether application of the empirical rule to the data set is appropriate. Explain your answers.
What does Chebyshev's rule say about the percentage of observations in any data set that lie within
(a) six standard deviations to either side of the mean?
(b) 1.5 standard deviations to either side of the mean?
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