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: 6.17 6.05 5.89 5.94 7.31 7.18 7.06 5.79 6.24 5.91 6.14 Use a calculator to verify that, for the preceding data, s2=0.318. Another random sample of years for a second plot gave the following annual wheat straw production (in pounds): 6.85 7.71 8.23 6.01 7.22 5.58 5.47 5.86 Use a calculator to verify that, for these data, s2=1.078. 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 significance. Assume that the data values in each problem come from independent populations and that each population follows a normal distribution. What is the level of significance? State the null and alternate hypotheses. Find the value of the sample F statistic. What are the degrees of freedom? What assumptions are you making about the original distribution? Find or estimate the P-value of the sample test statistic. Based on your answers in parts (1), (2), and (3), will you reject or fail to reject the null hypothesis?
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:
|
6.17 |
6.05 |
5.89 |
5.94 |
7.31 |
7.18 |
|
7.06 |
5.79 |
6.24 |
5.91 |
6.14 |
Use a calculator to verify that, for the preceding data, s2=0.318.
Another random sample of years for a second plot gave the following annual wheat straw production (in pounds):
|
6.85 |
7.71 |
8.23 |
6.01 |
7.22 |
5.58 |
5.47 |
5.86 |
Use a calculator to verify that, for these data, s2=1.078.
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 significance. Assume that the data values in each problem come from independent populations and that each population follows a
- What is the level of significance? State the null and alternate hypotheses.
- Find the value of the sample F statistic. What are the degrees of freedom? What assumptions are you making about the original distribution?
- Find or estimate the P-value of the sample test statistic.
- Based on your answers in parts (1), (2), and (3), will you reject or fail to reject the null hypothesis?
F-test:
It is the hypothesis testing for the variance of two populations are equal or different. By the variance of both the population or sample finding the ratio gives the test statistics 'f'. The f-distribution gives the value of the critical region to compare with the test statistics. In order to do it, the requirements are the level of significance, degrees of freedom of both the samples or the populations.
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