Need help with part c d and e Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year, many small plots of equal size but different soil/fertilizerconditions 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 4.423.89 3.87 4.12 3.09 4.86 2.90 5.01 3.39Verify 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 4.013.59 4.29 3.78 3.19 3.84 3.91 3.66 4.35Verify 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 ofsignificance.(a) What is the level of significance?0.05State the null and alternate hypotheses.OH: 0₁₂2=0₂: 0₂²; H₂:2OH: 0₁ #12:0₁ ² #020₂Ha = 0,₁²: 0₂² ; H₂:20₁²; H₂ : 0₂²= 0₂²; H ₂ : 0 ₁ ² 0₂²OH: 0₂² 0₁²Ho₂: (b) Find the value of the sample F statistic. (Use 2 decimal places.)3.41What are the degrees of freedom?df15numerator15denominatordfWhat assumptions are you making about the original distribution?O The populations follow independent normal distributions.O The populations follow independent normal distributions. We have random samples from each population.O The populations follow dependent normal distributions. We have random samples from each population.O The populations follow independent chi-square distributions. We have random samples from each population.(c) Find the P-value of the test. (Use 4 decimal places.)(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?O At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.O At the x = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.O At the x = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the a= 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.O Fail to reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.O Reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.O Reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.O Fail to reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.

Question

Need help with part c d and e Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year, many small plots of equal size but different soil/fertilizerconditions 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 4.423.89 3.87 4.12 3.09 4.86 2.90 5.01 3.39Verify 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 4.013.59 4.29 3.78 3.19 3.84 3.91 3.66 4.35Verify 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 ofsignificance.(a) What is the level of significance?0.05State the null and alternate hypotheses.OH: 0₁₂2=0₂: 0₂²; H₂:2OH: 0₁ #12:0₁ ² #020₂Ha = 0,₁²: 0₂² ; H₂:20₁²; H₂ : 0₂²= 0₂²; H ₂ : 0 ₁ ² > 0₂²OH: 0₂² 0₁²Ho₂: (b) Find the value of the sample F statistic. (Use 2 decimal places.)3.41What are the degrees of freedom?df15numerator15denominatordfWhat assumptions are you making about the original distribution?O The populations follow independent normal distributions.O The populations follow independent normal distributions. We have random samples from each population.O The populations follow dependent normal distributions. We have random samples from each population.O The populations follow independent chi-square distributions. We have random samples from each population.(c) Find the P-value of the test. (Use 4 decimal places.)(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?O At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.O At the x = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.O At the x = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the a= 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.O Fail to reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.O Reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.O Reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.O Fail to reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.

Accepted Answer

Let X and Y be the two populations for one plot and the second plotLet  be the two population…