SOLUTION: 2. A scientist wants to compare two delicate weighing instruments by repeated weighing of the same object. The first scale is used 30 times and the weights have a standard deviatio

Algebra ->  Probability-and-statistics -> SOLUTION: 2. A scientist wants to compare two delicate weighing instruments by repeated weighing of the same object. The first scale is used 30 times and the weights have a standard deviatio      Log On


   

Question 333313: 2. A scientist wants to compare two delicate weighing instruments by repeated weighing of the same object. The first scale is used 30 times and the weights have a standard deviation of 72 milligrams. The second scale is used 41 times and the weights have a standard deviation of 98 milligrams. At the 0.05 significance level, test the claim that the second scale produces greater variance.
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
To test the hypothesis of two variances use the F distribution and a test statistic F=max%28s%5B1%5D%5E2%2Cs%5B2%5D%5E2%29%2Fmin%28s%5B1%5D%5E2%2Cs%5B2%5D%5E2%29
---
Ho: sigma%5B1%5D%5E2=sigma%5B2%5D%5E2
Ha: sigma%5B1%5D%5E2%3C%3Esigma%5B2%5D%5E2
at alpha=0.05
--
critical value:
test statistic F=+98%5E2%2F72%5E2=1.853
--
reject Ho if test statistic > critical value
since test statistic = 1.853 > critical value=1.806 then reject Ho
--
conclusion:
at the alpha=0.05 level, the evidence suggest that sigma%5B1%5D%5E2%3C%3Esigma%5B2%5D%5E2