Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows.6.895.986.056.057.317.187.065.796.245.916.14Use a calculator to verify that, for this plot, the sample variance is s2 ≈ 0.324.Another random sample of years for a second plot gave the following annual wheat production (in pounds).7.735.776.128.087.225.585.475.86Use a calculator to verify that the sample variance for this plot is s2 ≈ 1.074.Test the claim that there is a difference (either way) in the population variance of wheat straw production for these two plots. Use a 5% level of signifcance.(a) What is the level of significance?State the null and alternate hypotheses.Ho: ?12 = ?22; H1: ?12 > ?22Ho: ?12 > ?22; H1: ?12 = ?22 Ho: ?22 = ?12; H1: ?22 > ?12Ho: ?12 = ?22; H1: ?12 ≠ ?22(b) Find the value of the sample F statistic. (Use 2 decimal places.)What are the degrees of freedom?dfN dfD What assumptions are you making about the original distribution?The populations follow independent normal distributions.The populations follow independent normal distributions. We have random samples from each population. The populations follow dependent normal distributions. We have random samples from each population.The populations follow independent chi-square distributions. We have random samples from each population.(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)p-value > 0.2000.100 < p-value < 0.200 0.050 < p-value < 0.1000.020 < p-value < 0.0500.002 < p-value < 0.020p-value < 0.002(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.(e) Interpret your conclusion in the context of the application.Fail to reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.Reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots. Reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.Fail to reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.

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Description: Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows.6.895.986.056.057.317.187.065.796.245.916.14Use a calcul

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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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Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows.

6.89	5.98	6.05	6.05	7.31	7.18
7.06	5.79	6.24	5.91	6.14

Use a calculator to verify that, for this plot, the sample variance is s² ≈ 0.324.

Another random sample of years for a second plot gave the following annual wheat production (in pounds).

7.73

5.77

6.12

8.08

7.22

5.58

5.47

5.86

Use a calculator to verify that the sample variance for this plot is s² ≈ 1.074.

Test the claim that there is a difference (either way) in the population variance of wheat straw production for these two plots. Use a 5% level of signifcance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: ?₁² = ?₂²; H₁: ?₁² > ?₂²H_o: ?₁² > ?₂²; H₁: ?₁² = ?₂² H_o: ?₂² = ?₁²; H₁: ?₂² > ?₁²H_o: ?₁² = ?₂²; H₁: ?₁² ≠ ?₂²

(b) Find the value of the sample F statistic. (Use 2 decimal places.)

What are the degrees of freedom?

df_N
df_D

What assumptions are you making about the original distribution?

The populations follow independent normal distributions.The populations follow independent normal distributions. We have random samples from each population. The populations follow dependent normal distributions. We have random samples from each population.The populations follow independent chi-square distributions. We have random samples from each population.

p-value > 0.2000.100 < p-value < 0.200 0.050 < p-value < 0.1000.020 < p-value < 0.0500.002 < p-value < 0.020p-value < 0.002

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.Reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots. Reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.Fail to reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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