A machine that fills beverage cans is to be replaced by a new system if the variance in the new machine has a variance of less than 0.01 when filling up 12 ounces of beverage in a can. In order to test the variance in the new machine 10 cans are filled and the amount of liquid in each can is measured to be:
12.09,11.97,12.05,12.03,11.96
11.93,12.03,12.06,12.08,11.95
a) Using fixed-level test, determine whether the specification is met at a level of significance of alpha =0.05 ?
b) Determine the corresponding P-value (or the corresponding bounds for it).
c) Based on the hypothesis testing statement presented in your solution, determine the corresponding bound (or bounds) for the variance of the population of this new model of scales.
Start your solution by clearly stating the null and alternative hypotheses, show all your calculations, and then clearly state your conclusion, simply stating "reject null hypothesis" or "fail to reject null hypothesis" is not considered a clear statement of conclusion. ( 25 pts.)
To speed up your calculations use Sigma (x_(i)-(ar{x} ))^(2)=0.03005.
sigma ^(2)<=0.009024
a variance of less than 0.01 when filling up 12 ounces of beverage in a can. In order to test the variance in the new machine 10 cans are filled and the amount of liquid in each can is measured to be: 12.09,11.97,12.05,12.03, 11.96 11.93,12.03,12.06,12.08.11.95
a)Using fixed-level test, determine whether the specification is met at a level of significance of = 0.05? b)Determine the corresponding P-value (or the corresponding bounds for it). c) Based on the hypothesis testing statement presented in your solution, determine the corresponding bound (or bounds) for the variance of the population of this new model of scales. Start your solution by clearly stating the null and alternative hypotheses, show all your calculations, and then clearly state your conclusion, simply stating "reject null hypothesis " or "fail to reject null hypothesis " is not considered a clear statement of conclusion. (25 pts.) To speed up your calculations use (x;-x=0.03005.
-20.009024