Answered: The FDA conducted a study to determine…

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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The FDA conducted a study to determine whether corn in a certain region contained unhealthy levels of pesticides. A biologist classified pesticide levels greater than 6.0 parts per million (ppm) as unhealthy. The pesticide levels of a random sample of 23 bushels in the region were measured and recorded. The data are shown in the stemplot below.

Pesticide Levels

2 | 8

3 | 0

3 | 5 8 8

4 | 1 1 2

4 | 6 8 8

5 | 0 1 2 2 3 4

5 | 9 9

6 | 3 4

6 | 6 8

Key: 2 | 8 = 2.8 ppm

What proportion of bushels of corn in the sample had pesticide levels that are classified by the biologist as unhealthy?

The mean pesticide level of the 23 bushels of corn in the sample was 4.90 ppm and the standard deviation was 1.12 ppm.

Construct and interpret a 95 percent confidence interval for the mean pesticide level of corn in the region

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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