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Name: The data below are yields for two different types of corn seed that we
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Description: The data below are yields for two different types of corn seed that were used on adjacent plots of land. Assume that the data are simple random samples and that the differences have a distribution that is approximately normal. Construct a 95% confid

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 data below are yields for two different types of corn seed that were used on adjacent plots of land. Assume that the data are simple random samples and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval estimate of the difference between type 1 and type 2 yields. What does the confidence interval suggest about farmer Joe's claim that type 1 seed is better than type 2 seed?

Type_1 Type_2
2047 2018
1961 1981
2135 2063
2445 2449
2285 2191
1957 1959
2112 2148
1422 1441

In this example, μd is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the type 1 seed yield minus the type 2 seed yield.

The 95% confident interval is __ <μd< __.

(round to two decimal places as needed)

What does the confidence interval suggest about farmer Joe's claim that type 1 seed is better than type 2 seed?

A. Because the confidence interval includes zero, there is sufficient evidence to support farmer Joe's claim.

B. Because the confidence interval only includes positive values and does not includezero, there is sufficient evidence to support farmer Joe's claim. This is the correct answer.

C. Because the confidence interval includes zero, there is not sufficient evidence to support farmer Joe's claim.

D. Because the confidence interval only includes positive values and does not include zero, there is not sufficient evidence to support farmer Joe's claim.

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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