Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. Suppose for a random sample of years, one plot gave the following annual wheat production (in pounds): 3.81 2.97 5.19 3.40 3.05 2.40 4.35 3.00 4.89 5.23 3.37 4.00 3.84 5.42 5.09 5.03 For this plot, the sample variance is . Another random sample of years for a second plot gave the following annual wheat production (in pounds): 3.53 3.65 3.89 4.19 3.44 3.42 3.58 3.83 3.46 4.32 3.58 3.45 3.77 3.54 3.48 4.07 For this plot, the sample variance is . Test the claim using that the population variance of annual wheat production for the first plot is larger than that for the second plot. Find (or estimate) the P-value of the sample test statistic given that the sample test statistic
Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. Suppose for a random sample of years, one plot gave the following annual wheat production (in pounds):
|
3.81 |
2.97 |
5.19 |
3.40 |
3.05 |
2.40 |
4.35 |
3.00 |
|
4.89 |
5.23 |
3.37 |
4.00 |
3.84 |
5.42 |
5.09 |
5.03 |
For this plot, the sample variance is . Another random sample of years for a second plot gave the following annual wheat production (in pounds):
|
3.53 |
3.65 |
3.89 |
4.19 |
3.44 |
3.42 |
3.58 |
3.83 |
|
3.46 |
4.32 |
3.58 |
3.45 |
3.77 |
3.54 |
3.48 |
4.07 |
For this plot, the sample variance is . Test the claim using that the population variance of annual wheat production for the first plot is larger than that for the second plot.
Find (or estimate) the P-value of the sample test statistic given that the sample test statistic .
| Sample 1 | Sample 2 | |
| 3.81 | 3.53 | |
| 2.97 | 3.65 | |
| 5.19 | 3.89 | |
| 3.4 | 4.19 | |
| 3.05 | 3.44 | |
| 2.4 | 3.42 | |
| 4.35 | 3.58 | |
| 3 | 3.83 | |
| 4.89 | 3.46 | |
| 5.23 | 4.32 | |
| 3.37 | 3.58 | |
| 4 | 3.45 | |
| 3.84 | 3.77 | |
| 5.42 | 3.54 | |
| 5.09 | 3.48 | |
| 5.03 | 4.07 | |
| 0.9589 | 0.0813 | Variance |
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