Question

12) A "Filler" fills 16-ounce bottles with beer. For the “Filler" to operate properly, the standard deviation of the population must be less than or equal to 0.04. A random sample of 10 bottles is selected, and the number of ounces of beer in each bottle recorded. At a = .01, can we reject the claim that the "Filler" is operating properly. 16.02 16.04 16.01 15.99 15.97 15.96 15.94 16.05 16.02 16.05

Answer 1

For the given data set, S (S-D)= = (x; -272 0.03866 NI Hoor < 0.0.4 → claim . Null hypothesis Alternative hypothesis HA : :r>0.04 Test statistic (X²) (n-1) s² 2 o . 2² 9 X 0.03866 0.042 = 8.407 xocolga 0.0199 Rejection criteria Reject Ho il te > Reject to if 8.407 > 21.665 [ 16.049 = 21.665 (source – STATKEY (image attached Conclusion As the above conclusion is not being satisfical , we fail to Reject the null hypothusis at 1 of level of significanu and conclude that the claim that the "Filler is operating property is true. (so it cannot be rejected)

Statkey Theoretical Distribution Chi-squared Distribution Reset Plot Chi-squared Distribution Left Tail Two-Tail Right Tail df 0.10 9 Edit Parameters 0.08 0.06 0.010 0.04 0.02 0.00 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 25.0 22.5 21.665 Activate Windows

The test statistic is calculated using the formula mentioned. The critical value is obtained from STATKEY (image attached for reference). We compare the test statistic with the critical value and make the required decision.