Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year, many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. For a random sample of years, one plot gave the following annual wheat production (in pounds). 4.26 3.78 4.08 3.63 4.05 3.79 4.09 4.42 3.89 3.87 4.12 3.09 4.86 2.90 5.01 3.39 Verify that, for this plot, the sample variance is s² = 0.311110. Another random sample of years for a second plot gave the following annual wheat production (in pounds). 3.64 3.61 3.46 3.79 4.00 3.72 4.13 4.01 3.59 4.29 3.78 3.19 3.84 3.91 3.66 4.35 Verify that the sample variance for this plot is s2 0.091166. ************ Test if there is a significant difference in the population variances of annual wheat production for the first plot versus the second plot. Use a 5% level of significance (a) What is the level of significance? State the null and alternate hypotheses. 2 OH: #0₂² 52₂2²; H₂ : 01² OH: 0₁²0₂²; H₂:0₁ ² = 0₂² OH: 0₂2>0₁2; H₂ : 0₂2² = 0₁² OH: 0₁₂²=0₂22²; H₂:0₂ ² > 0₂² = (b) Find the value of the sample F statistic. (Use 2 decimal places.)
Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year, many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. For a random sample of years, one plot gave the following annual wheat production (in pounds). 4.26 3.78 4.08 3.63 4.05 3.79 4.09 4.42 3.89 3.87 4.12 3.09 4.86 2.90 5.01 3.39 Verify that, for this plot, the sample variance is s² = 0.311110. Another random sample of years for a second plot gave the following annual wheat production (in pounds). 3.64 3.61 3.46 3.79 4.00 3.72 4.13 4.01 3.59 4.29 3.78 3.19 3.84 3.91 3.66 4.35 Verify that the sample variance for this plot is s2 0.091166. ************ Test if there is a significant difference in the population variances of annual wheat production for the first plot versus the second plot. Use a 5% level of significance (a) What is the level of significance? State the null and alternate hypotheses. 2 OH: #0₂² 52₂2²; H₂ : 01² OH: 0₁²0₂²; H₂:0₁ ² = 0₂² OH: 0₂2>0₁2; H₂ : 0₂2² = 0₁² OH: 0₁₂²=0₂22²; H₂:0₂ ² > 0₂² = (b) Find the value of the sample F statistic. (Use 2 decimal places.)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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Need help in part a and b
Transcribed Image Text:*************
Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year, many small plots of equal size but different soil/fertilizer conditions
are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. For a random sample of years, one plot gave
the following annual wheat production (in pounds).
4.26 3.78 4.08 3.63 4.05 3.79 4.09 4.42
3.89 3.87 4.12 3.09 4.86 2.90 5.01 3.39
Verify that, for this plot, the sample variance is s² = 0.311110.
Another random sample of years for a second plot gave the following annual wheat production (in pounds).
3.64 3.61 3.46 3.79 4.00 3.72 4.13 4.01
3.59 4.29 3.78 3.19 3.84 3.91 3.66 4.35
Verify that the sample variance for this plot is s2 0.091166.
Test if there is a significant difference in the population variances of annual wheat production for the first plot versus the second plot. Use a 5% level of significance.
(a) What is the level of significance?
2
State the null and alternate hypotheses.
OH: 0₁²=0₂22²; H₂0₁²
OH: 0₁²0₂2; H₂ : 0 ₁ ² = 0 ₂ ²
2
#
OH: 0₂²>0₁2; H₂ : 0 ₂ ² = 0 ₁²
1
OH₂:0₁₂²=0₂²2²; ₂: 0₁² > 0₂²
(b) Find the value of the sample F statistic. (Use 2 decimal places.)
What are the degrees of freedom?
df
numerator
denominator
df
What assumptions are you making about the original distribution?
O The populations follow independent normal distributions.
dont normal distributions. We have random samples from each population.
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