Confidence Intervals – Dr. Richards is researching the effectiveness of several new, organic types of fertilizer that are also good for the environment. In her sampling, she finds that the mean improvement in crop yields from three different fertilizers are all 23%. However, the 95% confidence intervals of the three fertilizers differ as follows: FertilizerMean Crop Yield Improvement95% Confidence Interval for Yield Improvement123%22% - 24%223%20% - 26%323%18% - 28% Explain what this it means to have the same sample means but different confidence intervals. What are the implications for Dr. Richards research?

In this situation the effectiveness of several new, organic types of fertilizer has been tested and…

Answered: Confidence Intervals – Dr. Richards is…

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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Confidence Intervals – Dr. Richards is researching the effectiveness of several new, organic types of fertilizer that are also good for the environment. In her sampling, she finds that the mean improvement in crop yields from three different fertilizers are all 23%. However, the 95% confidence intervals of the three fertilizers differ as follows:

Fertilizer	Mean Crop Yield Improvement	95% Confidence Interval for Yield Improvement
1	23%	22% - 24%
2	23%	20% - 26%
3	23%	18% - 28%

Explain what this it means to have the same sample means but different confidence intervals. What are the implications for Dr. Richards research?

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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