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. The following data are based on information taken from an article by G. A. Wiebe in the Journal of Agricultural Research (Vol. 50, pp. 331–357). For a random sample of years, one plot gave the following annual wheat production (in pounds):

Use a calculator to verify that, for this plot, the sample variance is s² ≈ 0.332.

Another random sample of years for a second plot gave the following annual wheat production (in pounds):

Use a calculator to verify that the sample variance for this plot is s² ≈ 0.089.

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?

Please provide the following information.

(a) What is the level of signi­ficance? State the null and alternate hypotheses.

(b) Find the value of the sample F statistic. What are the degrees of freedom?

What assumptions are you making about the original distribution?

(c) Find or estimate the P-value of the sample test statistic.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

(e) Interpret your conclusion in the context of the application.

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15 4.21 4.27 3.55 3.50 3.794.094.42 3.89 3.87 4.12 3.09 4.86 2.90 5.0 3.39 4.03 3.77 3.49 3.76 3.6 3.72 4.3 4.01 59 4.29 3.78 3.19 3.84 3.9 3.66 4.35