Answered: A particular moth can infest avocado…

Name: Show all your work. Indicate clearly the methods you use, because you
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Description: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. A particular moth can infest avocado trees and poten

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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Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

A particular moth can infest avocado trees and potentially damage the avocado fruit. A farmer plans to investigate the number of damaged avocado fruit on moth-infested avocado trees of a certain variety. A recent article states that the population distribution of the number of damaged avocado fruit on moth-infested avocado trees of this variety is symmetric but not mound-shaped with mean μ =59 and standard deviation σ = 24

(a) Compare the shapes of the sampling distributions of the sample mean number of damaged avocado fruit for random samples of 6 moth-infested trees and for random samples of 90 moth-infested trees from the population.

(b) Which of the following would be less likely to obtain from the population?

• A random sample of 36 moth-infested avocado trees having a mean number of damaged avocado fruit that is less than 60

• A random sample of 81 moth-infested avocado trees having a mean number of damaged avocado fruit that is less than 60

Justify your answer.

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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