Introduction to Probability and Statistics

14th Edition

ISBN: 9781133103752

Author: Mendenhall, William

Publisher: Cengage Learning

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Chapter 11.8, Problem 11.40E

Digitalis and Calcium Uptake A study was conducted to compare the effects of three levels of digitalis on the levels of calcium in the heart muscles of dogs. Because general level of calcium uptake vanes from one animal to another, the tissue for a heart muscle was regarded as a block, and comparisons of the three digitalis levels (treatments) were made within a given animal. The calcium uptakes for the three levels of digitalis, A, B, and C, were compared based on the heart muscles of four dogs and the results are given in the table. Use the Excel printout to answer the questions.
Chapter 11.8, Problem 11.40E, Digitalis and Calcium Uptake A study was conducted to compare the effects of three levels of , example 1

a. How many degrees of freedom are associated with SSE’?

b. Do the data present sufficient evidence to indicate a difference in the mean uptakes of calcium for the three levels of digitalis?

c. Use Tukey’s method of paired comparisons with α = 0.1 to rank the mean calcium uptakes for the three levels of digitalis.

d. Do the data indicate a difference in the mean uptakes of calcium for the tour heart muscles’?

e. Use Tukey’s method of paired comparisons with α = 0.1 to rank the mean calcium uptakes for the heart muscles of the four dogs used in the experiment. Are these results of any practical value to the researcher’?

f. Give the standard error of the difference between the mean calcium uptakes for two level of digitalis.

g. Find a 95% confidence interval for the difference in mean responses between treatments A and B.

Chapter 11.8, Problem 11.40E, Digitalis and Calcium Uptake A study was conducted to compare the effects of three levels of , example 2

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 11.8, Problem 11.39E

Chapter 11.8, Problem 11.41E

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Chapter 11 Solutions

Introduction to Probability and Statistics

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