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
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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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F003cc70c-1b75-4753-a416-fe02387aef72%2F6220dd33-3db1-423d-b34e-c3ee718d1f12%2Fpyn2m7h_processed.jpeg&w=3840&q=75)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F003cc70c-1b75-4753-a416-fe02387aef72%2F6220dd33-3db1-423d-b34e-c3ee718d1f12%2Fbygmqhd_processed.jpeg&w=3840&q=75)
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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