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.

5.91	6.68	6.75	6.96	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 ≈ 0.312.

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

6.05

6.33

6.26

6.96

7.22

5.58

5.47

5.86

Use a calculator to verify that the sample variance for thisplot is s² ≈ 0.385.

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 of significance?

State the null and alternate hypotheses.

H_o: σ₁² =σ₂²; H₁:σ₁² >σ₂²

H_o: σ₁² >σ₂²; H₁:σ₁² =σ₂²

H_o: σ₂² =σ₁²; H₁:σ₂² >σ₁²

H_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 follow dependent 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 > 0.200

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 the α = 0.05 level, we reject the null hypothesisand conclude the data are statisticallysignificant.     

At the α = 0.05 level, we fail to reject the nullhypothesis and conclude the data are not statisticallysignificant.

At the α = 0.05 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 differs between thetwo plots.

Reject the null hypothesis, there is insufficient evidence thatthe variance in annual wheat production differs between the twoplots.     

Reject the null hypothesis, there is sufficient evidence thatthe variance in annual wheat production differs between the twoplots.

Fail to reject the null hypothesis, there is insufficientevidence that the variance in annual wheat production differsbetween the two plots.