Mathematical Statistics with Applications

7th Edition

ISBN: 9780495110811

Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer

Publisher: Cengage Learning

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Textbook Question

Chapter 13.13, Problem 72E

Refer to Exercise 13.45. Answer part (b) by constructing an F test, using complete and reduced linear models.

13.45 An experiment was conducted to determine the effect of three methods of soil preparation on the first-year growth of slash pine seedlings. Four locations (state forest lands) were selected, and each location was divided into three plots. Because soil fertility within a location was likely to be more homogeneous than between locations, a randomized block design was employed, using locations as blocks. The methods of soil preparation were A (no preparation), B (light fertilization), and C (burning). Each soil preparation was randomly applied to a plot within each location. On each plot the same number of seedlings was planted, and the observation recorded was the average first-year growth (in centimeters) of the seedlings on each plot. These observations are reproduced in the accompanying table.

Chapter 13.13, Problem 72E, Refer to Exercise 13.45. Answer part (b) by constructing an F test, using complete and reduced

a Conduct an ANOVA. Do the data provide sufficient evidence to indicate differences in the mean growth for the three soil preparations?
b Is there evidence to indicate differences in mean growth for the four locations?

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 13.13, Problem 71E

Chapter 13, Problem 73SE

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Chapter 13 Solutions

Mathematical Statistics with Applications

Ch. 13.2 - The reaction times for two different stimuli in a...Ch. 13.2 - Prob. 2E Ch. 13.4 - State the assumptions underlying the ANOVA of a...Ch. 13.4 - Prob. 4E Ch. 13.4 - Prob. 5E Ch. 13.4 - Suppose that independent samples of sizes n1, n2,,...Ch. 13.4 - Four chemical plants, producing the same products...Ch. 13.4 - Prob. 8E Ch. 13.4 - Prob. 9E Ch. 13.4 - A clinical psychologist wished to compare three...

Ch. 13.4 - It is believed that women in the postmenopausal...Ch. 13.4 - If vegetables intended for human consumption...Ch. 13.4 - One portion of the research described in a paper...Ch. 13.4 - The Florida Game and Fish Commission desires to...Ch. 13.4 - Prob. 15E Ch. 13.4 - An experiment was conducted to examine the effect...Ch. 13.5 - Prob. 17E Ch. 13.5 - Refer to Exercise 13.17 and consider YiYi for i ...Ch. 13.5 - Refer to the statistical model for the one-way...Ch. 13.7 - Refer to Examples 13.2 and 13.3. a Use the portion...Ch. 13.7 - Refer to Examples 13.2 and 13.4. a Use the portion...Ch. 13.7 - a Based on your answers to Exercises 13.20 and...Ch. 13.7 - Refer to Exercise 13.7. a Construct a 95%...Ch. 13.7 - Prob. 24E Ch. 13.7 - Prob. 25E Ch. 13.7 - Prob. 26E Ch. 13.7 - Prob. 27E Ch. 13.7 - Prob. 28E Ch. 13.7 - Prob. 29E Ch. 13.7 - Prob. 30E Ch. 13.7 - Prob. 31E Ch. 13.7 - Prob. 32E Ch. 13.7 - Prob. 33E Ch. 13.7 - Prob. 34E Ch. 13.7 - Prob. 35E Ch. 13.8 - Prob. 36E Ch. 13.8 - Prob. 37E Ch. 13.8 - Prob. 38E Ch. 13.8 - Prob. 39E Ch. 13.8 - Prob. 40E Ch. 13.9 - Prob. 41E Ch. 13.9 - The accompanying table presents data on yields...Ch. 13.9 - Refer to Exercise 13.42. Why was a randomized...Ch. 13.9 - Prob. 44E Ch. 13.9 - Prob. 45E Ch. 13.9 - Prob. 46E Ch. 13.9 - Prob. 47E Ch. 13.9 - Prob. 48E Ch. 13.9 - Prob. 49E Ch. 13.9 - Prob. 50E Ch. 13.9 - Prob. 51E Ch. 13.10 - Prob. 52E Ch. 13.10 - Prob. 53E Ch. 13.10 - Prob. 54E Ch. 13.10 - Refer to Exercise 13.46. Construct a 95%...Ch. 13.10 - Prob. 56E Ch. 13.10 - Prob. 57E Ch. 13.11 - Prob. 58E Ch. 13.11 - Prob. 59E Ch. 13.11 - Prob. 60E Ch. 13.11 - Prob. 61E Ch. 13.11 - Prob. 62E Ch. 13.12 - Prob. 63E Ch. 13.12 - Prob. 64E Ch. 13.12 - Prob. 65E Ch. 13.12 - Prob. 66E Ch. 13.12 - Prob. 67E Ch. 13.12 - Prob. 68E Ch. 13.13 - Prob. 69E Ch. 13.13 - Prob. 70E Ch. 13.13 - Refer to Exercise 13.42. Answer part (a) by...Ch. 13.13 - Refer to Exercise 13.45. Answer part (b) by...Ch. 13 - Prob. 73SE Ch. 13 - Prob. 74SE Ch. 13 - Prob. 75SE Ch. 13 - Prob. 77SE Ch. 13 - A study was initiated to investigate the effect of...Ch. 13 - Prob. 79SE Ch. 13 - A dealer has in stock three cars (models A, B, and...Ch. 13 - In the hope of attracting more riders, a city...Ch. 13 - Prob. 84SE Ch. 13 - Prob. 85SE Ch. 13 - Prob. 86SE Ch. 13 - Prob. 87SE Ch. 13 - Prob. 88SE Ch. 13 - Prob. 89SE Ch. 13 - Prob. 90SE Ch. 13 - Prob. 92SE Ch. 13 - Prob. 94SE

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Solution Summary: The author analyzes whether there is sufficient evidence to indicate a difference in mean growth for the four locations using complete and reduced linear models.

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