Answered: What is the most appropriate test to…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 5E

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Caffeine is a common drug that affects the central nervous system. Among Problem 3.4 the issues involved with caffeine are how does it get from the blood to the brain, and does the presence of caffeine alter the ability of similar compounds to move across the blood-brain barrier? In this experiment, 15 lab rats were randomly assigned to one of 3 treatments (0, 5, and 10 mM of caffeine). Each treatment consisted of an arterial injection of C14-labeled adenine together with a concentration of caffeine (0 to 50 mM). Shortly after injection, the concentration of labeled adenine in the rat brains is measured as the response (data from McCall, Millington, and Wurtman 1982).

0 mM	5 mM	10 mM
5.74	5.92	3.05
6.9	3.66	1.94
3.86	4.62	1.23
6.94	3.47	3.45
6.49	1.33	1.61

What is the most appropriate test to determine if the three caffeine concentrations resulted to different mean adenine concentration of silage at 5% level of significance? Justify your answer.

Test to be used: ________________
Justification (Elaborate the assumptions and include only the p-values and conclusions for assumptions requiring test of hypothesis): ___________________

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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Follow-up Question

Suppose they conducted another set of experiment with increased sample size and saw that the three caffeine concentrations resulted to a different mean adenine concentration. Table below showed summary of Tukey’s HSD. Summarize the result of Tukey’s HSD in Table 2 and provide synthesis, given 5% level of significance.

Table 1. Matrix of HSD’s test result for the experiment

Treatments	Mean difference	p - value
0mM – 5mM	2.6283	<0.001 ***
0mM – 10mM	3.9383	0.0112 *
5mM – 10mM	1.3100	0.2458

Table 2. Summary of HSD’s result

Treatment	Mean	SD	Summary (in letter or in dot form)
0mM	6.0233	1.1508026
5mM	3.3950	1.8064855
10mM	2.0850	0.9490153

Synthesis:

________________________________________________________

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