In 1908, William Gosset published the article "The probable Error of a Mean" under the pseudonym of "Student". He included the data listed below for two different types of corn seed that were used on ad jacent plots of land. The listed values are the yields of head corn in pounds per acre. Use a 0.10 significance level to test the claim that the mean difference in yield between the two types of seed is 0. Regular 1903 1935 1910 2496 2108 1980 2060 1444 1612 1316 1511 Kiln dried 2009 1915 2011 2463 2180 1925 2122 1482 1542 1443 1535 a. Define the parameter A. mu Subscript d Baseline equals Mean of (Regular yield - Kiln dried yield) B. mu Subscript d Baseline equals Mean of the Regular yield C. mu Subscript d Baseline equals Mean of the Kiln dried yield D. mu equals Mean yield b. State the null and alternative hypotheses A. Upper H 0 : mu Subscript d Baseline equals 0 Upper H 1 : mu Subscript d Baseline greater than 0 B. Upper H 0 : mu equals 0 Upper H 1 : mu not equals 0 C. Upper H 0 : mu Subscript d Baseline equals 0 Upper H 1 : mu Subscript d Baseline less than 0 D. Upper H 0 : mu Subscript d Baseline equals 0 Upper H 1 : mu Subscript d Baseline not equals 0 c. Calculate the P-value. Which of these options is closest to its value? A. 0.238 B. 0.466 C. 0.152 D. 0.134 d. State the technical conclusion A. Do not reject Upper H 0 B. Reject Upper H 0

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Description: In 1908, William Gosset published the article "The probable Error of a Mean" under the pseudonym of "Student". He included the data listed below for two different types of corn seed that were used on ad jacent plots of land. The listed values are

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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In 1908, William Gosset published the article "The probable Error of a Mean" under the pseudonym of "Student". He included the data listed below for two different types of corn seed that were used on ad jacent plots of land. The listed values are the yields of head corn in pounds per acre. Use a 0.10 significance level to test the claim that the mean difference in yield between the two types of seed is 0.

Regular

1903

1935

1910

2496

2108

1980

2060	1444	1612	1316	1511
Kiln dried	2009	1915	2011	2463	2180	1925	2122	1482	1542	1443	1535

a. Define the parameter

mu Subscript d Baseline equals

Mean of (Regular yield - Kiln dried yield)

mu Subscript d Baseline equals

Mean of the Regular yield

mu Subscript d Baseline equals

Mean of the Kiln dried yield

mu equals

Mean yield

b. State the null and alternative hypotheses

Upper H 0 : mu Subscript d Baseline equals 0 Upper H 1 : mu Subscript d Baseline greater than 0

Upper H 0 : mu equals 0 Upper H 1 : mu not equals 0

Upper H 0 : mu Subscript d Baseline equals 0 Upper H 1 : mu Subscript d Baseline less than 0

Upper H 0 : mu Subscript d Baseline equals 0 Upper H 1 : mu Subscript d Baseline not equals 0

c. Calculate the P-value. Which of these options is closest to its value?

0.238

0.466

0.152

0.134

d. State the technical conclusion

Do not reject Upper H 0

Reject Upper H 0

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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