10th Edition

ISBN: 9780321989178

Author: Neil A. Weiss

Publisher: PEARSON

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A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Textbook Question

Chapter 9.6, Problem 161E

Delaying Adulthood. The convict surgeonfish is a common tropical reef fish that has been found to delay metamorphosis into adult by extending its larval phase. This delay often leads to enhanced survivorship in the species by increasing the chances of finding suitable habitat. In the paper “Delayed Metamorphosis of a Tropical Reef Fish (Acanthurus triostegus): A Field Experiment” (Marine Ecology Progress Series, Vol. 176, pp. 25–38), M. McCormick published data that he obtained on the larval duration, in days, of 90 convict surgeonfish. The data are given on the WeissStats site. At the 5% significance level, do the data provide sufficient evidence to conclude that the mean larval duration of convict surgeonfish exceeds 52 days?

a. Employ the Wilcoxon signed-rank test.
b. Employ the t-test.
c. Compare your results from parts (a) and (b).

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Chapter 9.6, Problem 160E

Chapter 9.6, Problem 162E

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Delaying Adulthood. The convict surgeonfish is a common tropical reef fish that has been found to delay metamorphosis into adult by extending its larval phase. This delay often leads to enhanced survivorship in the species by increasing the chances of finding suitable habitat. In the paper “Delayed Metamorphosis of a Tropical Reef Fish (Acanthurus triostegus): A Field Experiment” (Marine Ecology Progress Series, Vol. 176, pp. 25–38), M. McCormick published data that he obtained on the larval duration, in days, of 90 convict surgeonfish. The data are given on theWeissStats site. At the 5% significance level, do the data provide sufficient evidence to conclude that the mean larval duration of convict surgeonfish exceeds 52 days? a. Employ the Wilcoxon signed-rank test. b. Employ the t-test. c. Compare your results from parts (a) and (b).

SnowGoose Nests. In the article “Trophic Interaction Cycles in Tundra Ecosystems and the Impact of Climate Change” (Bio- Science, Vol. 55, No. 4, pp. 311–321), R. Ims and E. Fuglei provided an overview of animal species in the northern tundra. One threat to the snow goose in arctic Canada is the lemming. Snowy owls act as protection to the snow goose breeding grounds. For two years that are 3 years apart, the following graphs give relative frequency histograms of the distances, in meters, of snow goose nests to the nearest snowy owl nest. For each histogram, do the following: a. Identify the shape of the distribution with regard to modality. b. Identify the shape of the distribution with regard to symmetry (or nonsymmetry). c. If the distribution is unimodal and nonsymmetric, classify it as either right skewed or left skewed. d. Compare the two distributions.

Answer the exercise of the image. (In the other image are the final answers, this to verify the final answer).

Chapter 9 Solutions

Introductory Statistics (10th Edition)

Ch. 9.1 - Explain the meaning of the term hypothesis as used...Ch. 9.1 - Regarding the term null hypothesis: a. Originally,...Ch. 9.1 - What role does the decision criterion play in a...Ch. 9.1 - Suppose that you want to perform a hypothesis test...Ch. 9.1 - Suppose that you are considering a hypothesis test...Ch. 9.1 - Suppose that, in a hypothesis test, the null...Ch. 9.1 - Suppose that, in a hypothesis test, the null...Ch. 9.1 - What is the relation between the significance...Ch. 9.1 - Answer true or false and explain your answer: If...Ch. 9.1 - Answer true or false and explain your answer: For...

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Solution Summary: The author concludes that there is sufficient evidence to support the mean larval duration of convict surgeon fish at 5% level of significance.

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