Rothamsted Experimental Station (England) has studied wheatproduction since 1852. Each year, many small plots of equal sizebut different soil/fertilizer conditions are planted with wheat. Atthe end of the growing season, the yield (in pounds) of the wheaton the plot is measured. For a random sample of years, one plotgave the following annual wheat production (in pounds).

3.66	4.05	4.02	3.75	4.17	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 samplevariance is s² ≈ 0.307.

Another random sample of years for a second plot gave the followingannual wheat production (in pounds).

3.55	3.40	3.97	3.91	4.00	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 thisplot is s² ≈ 0.096.

Test the claim that the population variance of annual wheatproduction for the first plot is larger than that for the secondplot. Use a 1% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: σ₁² =σ₂²; H₁:σ₁² >σ₂²H_o:σ₁² >σ₂²; H₁:σ₁² =σ₂²Â Â Â Â H_o: σ₂² =σ₁²; H₁:σ₂² >σ₁²H_o:σ₁² =σ₂²; H₁:σ₁² ≠σ₂²

(b) Find the value of the sample F statistic. (Use 2decimal places.)


What are the degrees of freedom?

dfN
dfD

What assumptions are you making about the originaldistribution?

The populations follow independent normal distributions. We haverandom samples from each population. The populations followdependent normal distributions. We have random samples from eachpopulation.     The populations followindependent normal distributions. The populations followindependent chi-square distributions. We have random samples fromeach population.

(c) Find or estimate the P-value of the sample teststatistic. (Use 4 decimal places.)

p-value > 0.100 0.050 < p-value <0.100     0.025 < p-value <0.050 0.010 < p-value < 0.025 0.001 <p-value < 0.010 p-value < 0.001

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

At the α = 0.01 level, we reject the null hypothesisand conclude the data are not statistically significant. At theα = 0.01 level, we reject the null hypothesis and concludethe data are statistically significant.     Atthe α = 0.01 level, we fail to reject the null hypothesisand conclude the data are not statistically significant. At theα = 0.01 level, we fail to reject the null hypothesis andconclude the data are statistically significant.

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

Fail to reject the null hypothesis, there is sufficient evidencethat the variance in annual wheat production is greater in thefirst plot. Reject the null hypothesis, there is insufficientevidence that the variance in annual wheat production is greater inthe first plot.     Reject the null hypothesis,there is sufficient evidence that the variance in annual wheatproduction is greater in the first plot. Fail to reject the nullhypothesis, there is insufficient evidence that the variance inannual wheat production is greater in the first plot.