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):
3.06
4.97
5.01
4.13
5.02
2.91
3.88
2.55
5.18
3.68
4.54
2.65
4.14
5.11
3.19
Use a calculator to verify that the sample variance for this plot is s^2=0.923. Another random sample of years for a second plot gave the following annual wheat production (in pounds):
3.61
3.50
3.81
3.89
3.84
3.53
3.62
3.67
4.05
3.82
4.12
3.75
3.92
4.01
Use a calculator to verify that the sample variance for this plot is s^2=0.042. Suppose that we test the claim using a=0.01 that the population variance of annual wheat production for the first plot is larger than that for the second plot.
State the null and alternate hypotheses.
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