Answered: Table 2 gives the output for 8 cropping…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 54E: Conditional probability If 40 of the population have completed college, and 85 of college graduates...

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Question

Table 2 gives the output for 8 cropping seasons of Sweet Spring Country Farm that used each of 4 fertilizers. Assume that the outputs with each fertilizer are normally distributed with equal variance.

(a) Find the mean output for each fertilizer and the grand mean for all cropping seasons and for all four fertilizers.

(b) Estimate the population variance from the variance between the means or columns. Solve for SSA and MSA.

Fertilizer 1
Fertilizer 2
Fertilizer 3
Fertilizer 4
51
47
57
50
47
50
48
61
56
58
52
57
52
61
60
65
57
51
61
58
59
48
57
53
58
59
51
61
60
50
46
59
440
424
432
464

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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