A researcher is interested in studying mean gill beat rates for fish in water with three different levels of calcium. The results of the experiment are stored in below. Set up the null and alternative hypotheses. What is the mean square error? State the F-statistic of the test as well as the p-value of the test. What is the conclusion of the test, in context? Test which two levels of calcium are most likely to find a difference in mean gill rates. State all three pairwise hypothesis tests and the p-values for each test. Calcium GillRate Low 55 Low 63 Low 78 Low 85 Low 65 Low 98 Low 68 Low 84 Low 44 Low 87 Low 48 Low 86 Low 93 Low 64 Low 83 Low 79 Low 85 Low 65 Low 88 Low 47 Low 68 Low 86 Low 57 Low 53 Low 58 Low 47 Low 62 Low 64 Low 50 Low 45 Medium 38 Medium 42 Medium 63 Medium 46 Medium 55 Medium 63 Medium 36 Medium 58 Medium 73 Medium 69 Medium 55 Medium 68 Medium 63 Medium 73 Medium 45 Medium 79 Medium 41 Medium 83 Medium 60 Medium 48 Medium 59 Medium 33 Medium 67 Medium 43 Medium 57 Medium 72 Medium 46 Medium 74 Medium 68 Medium 83 High 59 High 45 High 63 High 52 High 59 High 78 High 72 High 53 High 69 High 68 High 57 High 63 High 68 High 83 High 38 High 85 High 68 High 63 High 58 High 48 High 42 High 42 High 80 High 42 High 52 High 37 High 57 High 62 High 40 High 42

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A researcher is interested in studying mean gill beat rates for fish in water with three different levels of calcium. The results of the experiment are stored in below.

Set up the null and alternative hypotheses. What is the mean square error?
State the F-statistic of the test as well as the p-value of the test. What is the conclusion of the test, in context?
Test which two levels of calcium are most likely to find a difference in mean gill rates. State all three pairwise hypothesis tests and the p-values for each test.

Calcium	GillRate
Low	55
Low	63
Low	78
Low	85
Low	65
Low	98
Low	68
Low	84
Low	44
Low	87
Low	48
Low	86
Low	93
Low	64
Low	83
Low	79
Low	85
Low	65
Low	88
Low	47
Low	68
Low	86
Low	57
Low	53
Low	58
Low	47
Low	62
Low	64
Low	50
Low	45
Medium	38
Medium	42
Medium	63
Medium	46
Medium	55
Medium	63
Medium	36
Medium	58
Medium	73
Medium	69
Medium	55
Medium	68
Medium	63
Medium	73
Medium	45
Medium	79
Medium	41
Medium	83
Medium	60
Medium	48
Medium	59
Medium	33
Medium	67
Medium	43
Medium	57
Medium	72
Medium	46
Medium	74
Medium	68
Medium	83
High	59
High	45
High	63
High	52
High	59
High	78
High	72
High	53
High	69
High	68
High	57
High	63
High	68
High	83
High	38
High	85
High	68
High	63
High	58
High	48
High	42
High	42
High	80
High	42
High	52
High	37
High	57
High	62
High	40
High	42

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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