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.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Problem 1P
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Need help in part a and b
![**Wheat Production Variance Analysis at Rothamsted Experimental Station**
Rothamsted Experimental Station in England has been studying wheat production since 1852. Each year, small plots of equal size but with different soil and fertilizer conditions are planted with wheat. The yield (in pounds) from these plots is measured at the end of the growing season. For one random sample, a plot yielded the following annual wheat production:
- 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
The sample variance for this plot is calculated as \( s^2 \approx 0.311110 \).
Another random sample for a second plot produced the following annual wheat production:
- 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
The sample variance for this plot is \( s^2 \approx 0.091166 \).
**Objective:**
Test if there is a significant difference in the population variances of wheat production between the first and second plots using a 5% level of significance.
(a) **Level of significance:**
[Input: Level of Significance]
State the null and alternate hypotheses:
- \( H_0: \sigma_1^2 = \sigma_2^2; H_a: \sigma_1^2 \neq \sigma_2^2 \)
- \( H_0: \sigma_2^2 \neq \sigma_1; H_a: \sigma_2 = \sigma_1 \)
- \( H_0: \sigma_2^2 > \sigma_1^2; H_a: \sigma_2 = \sigma_1 \)
- \( H_0: \sigma_1^2 = \sigma_2^2; H_a: \sigma_1^2 > \sigma](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F675d7c68-68c2-40f4-bb09-6fc638745853%2Fd914dce6-58d2-45f9-8094-a9a0d598fd3b%2Fmgjw5y9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Wheat Production Variance Analysis at Rothamsted Experimental Station**
Rothamsted Experimental Station in England has been studying wheat production since 1852. Each year, small plots of equal size but with different soil and fertilizer conditions are planted with wheat. The yield (in pounds) from these plots is measured at the end of the growing season. For one random sample, a plot yielded the following annual wheat production:
- 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
The sample variance for this plot is calculated as \( s^2 \approx 0.311110 \).
Another random sample for a second plot produced the following annual wheat production:
- 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
The sample variance for this plot is \( s^2 \approx 0.091166 \).
**Objective:**
Test if there is a significant difference in the population variances of wheat production between the first and second plots using a 5% level of significance.
(a) **Level of significance:**
[Input: Level of Significance]
State the null and alternate hypotheses:
- \( H_0: \sigma_1^2 = \sigma_2^2; H_a: \sigma_1^2 \neq \sigma_2^2 \)
- \( H_0: \sigma_2^2 \neq \sigma_1; H_a: \sigma_2 = \sigma_1 \)
- \( H_0: \sigma_2^2 > \sigma_1^2; H_a: \sigma_2 = \sigma_1 \)
- \( H_0: \sigma_1^2 = \sigma_2^2; H_a: \sigma_1^2 > \sigma
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