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What are the degrees of freedom? df 15 numerator df denominator What 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. 15 (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? At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. 0.05 level we fail to reject the pull hypothesis and conclude the data are statistically significant. At the

What are the degrees of freedom? df 15 numerator df denominator What 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. 15 (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? At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. 0.05 level we fail to reject the pull hypothesis and conclude the data are statistically significant. At the

MATLAB: An Introduction with Applications
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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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/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? 0.05 State the null and alternate hypotheses. OH: 0₁₂2=0₂ : 0₂²; H₂: 2 OH: 0₁ # 12:0₁ ² #02 0₂ Ha = 0,₁² : 0₂² ; H₂: 2 0₁²; H₂ : 0₂² = 0₂²; H ₂ : 0 ₁ ² > 0₂² OH: 0₂² 0₁² Ho₂:
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? 0.05 State the null and alternate hypotheses. OH: 0₁₂2=0₂ : 0₂²; H₂: 2 OH: 0₁ # 12:0₁ ² #02 0₂ Ha = 0,₁² : 0₂² ; H₂: 2 0₁²; H₂ : 0₂² = 0₂²; H ₂ : 0 ₁ ² > 0₂² OH: 0₂² 0₁² Ho₂:
(b) Find the value of the sample F statistic. (Use 2 decimal places.) 3.41 What are the degrees of freedom? df 15 numerator 15 denominator df What 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.
Transcribed Image Text:(b) Find the value of the sample F statistic. (Use 2 decimal places.) 3.41 What are the degrees of freedom? df 15 numerator 15 denominator df What 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.
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