df df What assumptions are you making about the original distribution? O The populations follow independent normal distributions. We have random samples trom cach population. O The populations follow independent chi-square distributions. We have tandon samples fram Fach pepulation. O The populations follow independent normal distributions. O The populations follow dependent normal distributions. We have random sampies from each population. (C) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places) Op value > 0.200 O 0.100 < p-value < 0.200 O 0.050 < p-value < 0.100 O 0.020 < p-value < 0.050 O 0.002

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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.
6.40
7.03
7.17
6.96
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 s2z 0.317.
Another random sarmple of years for a second plot gave the following annual wheat production (In pounds).
7.10
7.03
8.15
5.91
7.22 5,58 547
5.86
Use a calculator to verify that the sample variance for this plot is s0.g33.
Test the claim that there is a difterence (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?
0.05
State the null and alternate hypotheses.
O H, 0, = 0,2; H,0,> 0,?
O H, 0,> 0,; H,: 0,2 = 0,?
O Hoi 0,?-0,2; H;: 0, > ,?
(b) Find the value of the sample F statistic. (Use 2 decimal places.)
What are the degrees of freedom?
dfp
What assumptions are you making about the original distribution?
Transcribed Image Text: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. 6.40 7.03 7.17 6.96 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 s2z 0.317. Another random sarmple of years for a second plot gave the following annual wheat production (In pounds). 7.10 7.03 8.15 5.91 7.22 5,58 547 5.86 Use a calculator to verify that the sample variance for this plot is s0.g33. Test the claim that there is a difterence (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? 0.05 State the null and alternate hypotheses. O H, 0, = 0,2; H,0,> 0,? O H, 0,> 0,; H,: 0,2 = 0,? O Hoi 0,?-0,2; H;: 0, > ,? (b) Find the value of the sample F statistic. (Use 2 decimal places.) What are the degrees of freedom? dfp What assumptions are you making about the original distribution?
What are the degrees of freedom?
dfy
dfp
What assumptions are you making about the original distribution?
O The populatlons follow independent normal distributions. We have random samples trom cach population.
O The populations follow independent chi-square distributions. We have randorm samples from each pepulation.
O The populations follow independent normal distributions,
O The populations follow dependent 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.)
Op value > 0.200
O 0.100 < p-value < 0.200
O 0.050 < p-value < 0.100
O 0.020 < p-value < 0.050
O 0.002 < p value < 0.020
O p value < 0.002
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the nill hıypothesis?
O AL Lhe a
0.05 level, we reject the null hypothesis and conclude the data are nol slalislically significant.
O At the a - 0.05 level, we reject the null hypothesis and conclude the data arc statistically significant.
O AL the a - 0.05 level, we fail to reject the null hypothesis and conclude the data are ol slatistically significant.
O At the a - 0.05 level, we fail lu reject the null hypothesis and conclude the data arc statistically significant.
(e) Interpret your conclusion in the context of the application.
O lail to reject the rnull hypothesis, there is sufficient evidence that the varlance In annual wheat production differs between the two plots.
O Reject the null hypothesis, there is insufficient evidence that the variance in ainual wheat production differs between :he two plots.
O Reject the null hypothesis, there is sufficient evidence that thc varlance in annual wheat production differs between the two plots.
O tai to reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production diffors between the two plots.
Transcribed Image Text:What are the degrees of freedom? dfy dfp What assumptions are you making about the original distribution? O The populatlons follow independent normal distributions. We have random samples trom cach population. O The populations follow independent chi-square distributions. We have randorm samples from each pepulation. O The populations follow independent normal distributions, O The populations follow dependent 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.) Op value > 0.200 O 0.100 < p-value < 0.200 O 0.050 < p-value < 0.100 O 0.020 < p-value < 0.050 O 0.002 < p value < 0.020 O p value < 0.002 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the nill hıypothesis? O AL Lhe a 0.05 level, we reject the null hypothesis and conclude the data are nol slalislically significant. O At the a - 0.05 level, we reject the null hypothesis and conclude the data arc statistically significant. O AL the a - 0.05 level, we fail to reject the null hypothesis and conclude the data are ol slatistically significant. O At the a - 0.05 level, we fail lu reject the null hypothesis and conclude the data arc statistically significant. (e) Interpret your conclusion in the context of the application. O lail to reject the rnull hypothesis, there is sufficient evidence that the varlance In annual wheat production differs between the two plots. O Reject the null hypothesis, there is insufficient evidence that the variance in ainual wheat production differs between :he two plots. O Reject the null hypothesis, there is sufficient evidence that thc varlance in annual wheat production differs between the two plots. O tai to reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production diffors between the two plots.
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