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. For a random sample of years, one plot gave the following annual wheat production (in pounds).
3.75 | 4.20 | 3.90 | 3.66 | 3.63 | 3.79 | 4.09 | 4.42 |
3.89 | 3.87 | 4.12 | 3.09 | 4.86 | 2.90 | 5.01 | 3.39 |
Use a calculator to verify that, for this plot, the sample
variance is s2 ≈ 0.312.
Another random sample of years for a second plot gave the following
annual wheat production (in pounds).
3.52 | 3.52 | 4.09 | 3.73 | 4.03 | 3.72 | 4.13 | 4.01 |
3.59 | 4.29 | 3.78 | 3.19 | 3.84 | 3.91 | 3.66 | 4.35 |
Use a calculator to verify that the sample variance for this
plot is s2 ≈ 0.095.
Test the claim that the population variance of annual wheat
production for the first plot is larger than that for the second
plot. Use a 1% level of significance
H0:
H1:
The test statistic F = s1^2/s2^2
= 0.312/0.095 = 3.28
P-value = P(F > 3.28)
= 0.0138
Since the P-value is greater than the significance level(0.0138 > 0.01), so we should not reject H0.
At 1% significance level, there is not sufficient evidence to support the claim that the population variance of annual wheat production for the first plot is larger than the second plot.
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