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).

3.81	4.11	3.96	4.26	3.78	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 ≈ 0.305.

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

3.70	3.73	4.00	3.43	3.52	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 ≈ 0.095.

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> σ₂²

H_o:σ₁² >σ₂²;H₁: σ₁²= σ₂²Â Â Â Â 

H_o:σ₂² =σ₁²;H₁: σ₂²> σ₁²

H_o:σ₁² =σ₂²;H₁: σ₁²â‰  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 dependent normal distributions. We haverandom samples from each population.

The populations follow independent normal distributions. We haverandom samples from each population.    

The populations follow independent normal distributions.

The populations follow independent chi-square distributions. Wehave random samples from each 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 rejector fail to reject the null hypothesis?

At the α = 0.01 level, we reject the null hypothesisand conclude the data are not statistically significant.

At the α = 0.01 level, we reject the null hypothesisand conclude the data are statisticallysignificant.    

At the α = 0.01 level, we fail to reject the nullhypothesis and conclude the data are not statisticallysignificant.

At the α = 0.01 level, we fail to reject the nullhypothesis and conclude 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 insufficient evidence thatthe variance in annual wheat production is greater in the firstplot.    

Reject the null hypothesis, there is sufficient evidence thatthe variance in annual wheat production is greater in the firstplot.

Fail to reject the null hypothesis, there is insufficientevidence that the variance in annual wheat production is greater inthe first plot.