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Chapter 3: Q. 6 (page 151)
Data Set A has more variation than Data Set B. Decide which of the following statements are necessarily true.
a. Data Set A has a larger mean than Data Set B.
b. Data Set A has a larger standard deviation than Data Set B.
a. False
b. True
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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?
a) Determine the mode of the data.
b) Decide whether it would be appropriate to use either the mean or median as a measure of center. Explain your answer.
Medical School Faculty. The Association of American Medical College (AAMC) in a compiles data on medical school facility and publishes the results in AAMC Faculty Roster. The following table presents a frequency distribution of rank for medical school faculty during one year.
The Beatles. In the article. "Length of The Beatles' Songs",(Chance Vol. . No. , pp. ). T. Koyama discusses aspects and interpretations of the lengths of songs by The Beatles. Data on the length, in seconds, of Beatles' songs are presented on the Weiss Stats site.
The Great Gretzky. Wayne Giretzy, a retired professional hockey player, played 20 seasons in the National Hockey League (NHL), from 1980 through 1999 , S, Berry explored some of Gretaky"s accomplishmeats in "A Statistician Reads the Sports Pages" (Chanee, Vol, 16, Ne, 1. Pp. 49-54). The following table shoras the sumber of games in which Greuky played during each of has 20 seasons in the NHL.
The cheetah (Acinonyx jubatus) is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of miles per hour (mph) and. according to the online document "Cheetah Conservation in Southern Africa" by J. Urbaniak, the cheetah is capable of speeds up to The following table gives the top speeds, in miles per hour, arranged in increasing order, for a sample of cheetahs.
The sample mean and sample standard deviation of these speeds are and , respectively. A histogram of the speeds is bell shaped.
a. Is it reasonable to apply the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean?
b. Use the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean.
c. Use the data to obtain the exact percentages of observations that lie within one, two, and three standard deviations to either side of the mean.
d. Compare your answers in parts (b) and (c).
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