Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sumple 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 sz 0.317. Another random sample 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 5.47 5.86 Use a calculator to verify that the sample variance for this plot is s? x 0.933. 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. O H: 0, - 0,; H,: 0,2>0 (b) Find the value of the sample Fstatistic. (Use 2 decimal places.) What are the degrees of freedorm? df P Type here to search 75°F Mustly sunny A A - 4x 1103 AM
Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sumple 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 sz 0.317. Another random sample 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 5.47 5.86 Use a calculator to verify that the sample variance for this plot is s? x 0.933. 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. O H: 0, - 0,; H,: 0,2>0 (b) Find the value of the sample Fstatistic. (Use 2 decimal places.) What are the degrees of freedorm? df P Type here to search 75°F Mustly sunny A A - 4x 1103 AM
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Transcribed Image Text:Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sumple 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 s2 0.317.
Another random sample 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
5.47 5.86
Use a calculator to verify that the sample variance for this plot is s2 : 0.933.
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.
2.
O H 0,-0,; Hi o0,
2.
(b) Find the value of the sample Fstutistic. (Use 2 decimal places.)
What are the degrees of freedom?
P Type here to search
36
75°F Mustly sunny
11:03 AM
1/30/2021
to
ho
4+
DII
201
Transcribed Image Text:What are the degrees of freedom?
df N
df
What assumptions are you making about the original distribution?
O The populations follow independent normal distributions. We have random sarmples from each population.
O The populations follow independent chi-square distributions. We have random samples from cach population.
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.)
O p-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 ariswers in parts (a) to (c), will you reject or fail to reject the null hypothes s?
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a
0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the a - 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
O AL the a = 0.05 level, we fail to reject the null hypothesls 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 varlance in annual wheat production differs belween 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 varlance in annual wheat production differs between the two plots.
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