Mary bakes and sells rice crispies treats that she bakes ans

Mary bakes and sells rice crispies treats that she bakes ans cuts by hand. She bought a cutter tool, which she believes reduces the variation on the weight of the treats. The standard deviation before was 1.4 oz. By using the tool on 100 treats, she saw a standard devaition of 0.9 oz. At alpha = 0.01 test the claim that this tool actually reduces the standard deviation of these treats.

Solution

Ho: o=1.4
Ha: o^< 1.4
The test statistic is
Chisquare =(n-1)*s^2/o^2
=(100-1)*(0.9)^2/(1.4)^2
= 40.9133
Given a=0.01, the critical value of chisquare with , df=n-1= 100 - 1 = 99 is 69.229 (from chisquare table)
Since 69.229 is greater than 40.9133, we do not reject Ho.
So we can conclude that the variance in the weight of the treats are similar to the population