consistency3156.32234.3consistency

(a) What is the level of significance? 

State the null and alternate hypotheses.

Ho: σ12 = σ22; H1: σ12 > σ22

Ho: σ12 > σ22; H1: σ12 = σ22    

Ho: σ22 = σ12; H1: σ22 > σ12

Ho: σ12 = σ22; H1: σ12 ≠ σ22

(b) Find the value of the sample F statistic. (Round your answer to two decimal places.) 

What are the degrees of freedom?

dfN

dfD

What assumptions are you making about the original distribution? 

The populations follow independent normal distributions.

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

The populations follow independent chi-square distributions. We have random samples from each population.

The populations follow dependent normal distributions. We have random samples from each population.

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

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 or fail to reject the null hypothesis?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.    

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

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

Fail to reject the null hypothesis, there is sufficient evidence that the variance in consumption of gasoline is greater in the new fuel injection systems.

Reject the null hypothesis, there is insufficient evidence that the variance in consumption of gasoline is greater in the new fuel injection systems.    

Reject the null hypothesis, there is sufficient evidence that the variance in consumption of gasoline is different in both fuel injection systems.

Fail to reject the null hypothesis, there is insufficient evidence that the variance in consumption of gasoline is different in both fuel injection systems.

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