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 6 547 175 706 407 317 187 065 796 245 916 14 Use a calculator to verify that, for this plot, the sample variance is s 2 0 358 Another random sample of years for a second plot gave the following annual wheat production (in pounds) 5 776 127 315 987 225 585 475 86 Use a calculator to verify that the sample variance for this plot is s 2 0 505 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 1 2 2 2 H 1 1 2 2 2 H o 1 2 2 2 H 1 1 2 2 2 H o 2 2 1 2 H 1 2 2 1 2 H o 1 2 2 2 H 1 1 2 2 2 (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 chi square distributions We have random samples from each population The populations follow independent normal distributions The populations follow dependent normal distributions We have random samples from each population The populations follow independent normal 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 2000 050 p value 0 1000 020 p value 0 0500 002 p value 0 020 p 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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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

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.

6.547.175.706.407.317.187.065.796.245.916.14

Use a calculator to verify that, for this plot, the sample variance is s² 0.358.

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

5.776.127.315.987.225.585.475.86

Use a calculator to verify that the sample variance for this plot is s² 0.505.

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 = ₂²H_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 chi-square distributions. We have random samples from each population.The populations follow independent normal distributions.The populations follow dependent normal distributions. We have random samples from each population.The populations follow independent normal distributions. We have random samples from each population.

p-value > 0.2000.100 < p-value < 0.2000.050 < 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.