Answered: rtilizer: In an agricultural…

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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Question

Fertilizer: In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Twelve randomly selected plots of land were treated with fertilizer A, and

randomly selected plots were treated with fertilizer B. The number of pounds of harvested fruit was measured from each plot. Following are the results.

Fertilizer A
523	464	483	441	491	403
466	448	457	437	516	417

Fertilizer B
408	398	382	368	393
415

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Part 1 of 3

Explain why it is necessary to check whether the populations are approximately normal before constructing a confidence interval.

Since the sample size is ▼small, it is necessary to check that the populations are approximately normal.

Part 2 of 3

Following are boxplots of these data. Is it reasonable to assume that the populations are approximately normal?

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It ▼is reasonable to assume that the populations are approximately normal.

Part: 2 / 3

2 of 3 Parts Complete

Part 3 of 3

Construct a

90%

confidence interval for the difference between the mean yields for the two types of fertilizer. Let

μ1

denote the mean yield for fertilizer A. Use the TI-84 Plus calculator. Round the answers to one decimal place.

The

90%

confidence interval for the difference between the mean yields for the two types of fertilizer is

<μ1-μ2<

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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