Two plots at Rothamsted Experimental Station were studied forproduction of wheat straw. For a random sample of years, the annualwheat straw production (in pounds) from one plot was asfollows.

6.12	6.54	6.47	5.98	7.31	7.18
7.06	5.79	6.24	5.91	6.14

Use a calculator to verify that, for this plot, the samplevariance is s² ≈ 0.285.

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

5.91

6.75

7.03

6.12

7.22

5.58

5.47

5.86

Use a calculator to verify that the sample variance for thisplot is s² ≈ 0.449.

Test the claim that there is a difference (either way) in thepopulation variance of wheat straw production for these two plots.Use a 5% level of signifcance. (a) What is the level ofsignificance?

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

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

p-value > 0.200 0.100 < p-value <0.200     0.050 < p-value <0.100 0.020 < p-value < 0.050 0.002 <p-value < 0.020 p-value < 0.002

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

At the α = 0.05 level, we reject the null hypothesisand conclude the data are not statistically significant. At theα = 0.05 level, we reject the null hypothesis and concludethe data are statistically significant.     Atthe α = 0.05 level, we fail to reject the null hypothesisand conclude the data are not statistically significant. At theα = 0.05 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 differs between thetwo plots. Reject the null hypothesis, there is insufficientevidence that the variance in annual wheat production differsbetween the two plots.     Reject the nullhypothesis, there is sufficient evidence that the variance inannual wheat production differs between the two plots. Fail toreject the null hypothesis, there is insufficient evidence that thevariance in annual wheat production differs between the twoplots.