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Chapter 3: Q. 3.225 (page 149)

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?

Short Answer

Expert verified

a. The z-score for male lowland copperhead in Tasmania is 0.1149 and the z-score for male tiger snake in Tasmania is 0.3163

b. If the distributions of the two data have same shape then it is reasonable to use z score to compute the standings of the weight of two snakes.

c. The tiger snake of 580g is larger as compared to other tiger snakes than copperhead of 850g is to other copperheads.

Step by step solution

01

Finding z-score

The z-score for male lowland copperhead in Tasmania is

The z-score for male tiger snake in Tasmania is

02

Reasonability to use z score to compute the standings of the weight of two snakes.

It is reasonable to use z score to compute the standings of the weight of two snakes if the distributions of the two data have same shape.

03

Comparison of weights of the snakes

From part (a), the value of 850 is 0.115 standard deviation above the mean for lowland copper head snakes and value of 850 is 0.316 standard deviation above the mean for tiger snakes.

The tiger snake of 580g is larger as compared to other tiger snakes than copperhead of 850g is to other copperheads.

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