Question

The bottlers of a new soft drink are experiencing problems with the filling mechanism for their bottles and decide to test if true variance of the fill volume is 15 or not. The filled volume for 20 bottles was measured, yielding a sample variance of 20. Test the hypothesis at significance level 0.05.

Answer 1

The provided sample variance is s²=20 and the sample size is given by n=15.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:σ²=15

Ha:σ²≠15

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 the rejection region for this two-tailed test is R={χ²:χ²<5.629 or χ²>26.119}.

(3) Test Statistics

The Chi-Squared statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that χ_L²​=5.629<χ²=18.667<χ_U²​=26.119, 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 σ² is different than 15, at the 0.05 significance level.