Question

An automotive manufacturer believes that the variance of the gas milage for its hybrid vehicles is 6. You work for an energy conservation agency and want to test this claim . You find that a random sample of the miles per gallon of 28 of the manufacturer’s hybrid vehicles has a variance of 4.25. At α = 0.05 do you have enough evidence to reject the manufacturer’s claim?

Answer 1

The provided sample variance is and the sample size is given by n=28.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:

Ha:

This corresponds to a two-tailed test, for which a Chi-Square test for one population variance will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the rejection region for this two-tailed test is .

(3) Test Statistics

The Chi-Squared statistic is computed as follows:

(4) The decision about the null hypothesis

Since it is observed that , it is then concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population variance is different than 6, at the 0.05 significance level.

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