been stuck with this stats problem for an Hour!!

Question

Top sales executives, Alissa and Emilia came up with kiwi passion fruit cookie company. The machine fills each package cookies so that they have an average weight of 32 ounces with a variance of 0.015 square ounces. Chloe, a quality control inspector for the company took a random sample of 25 packages of the new cookie and got a sample variance of 0.029 square ounces. If she find that the machine fills the packages with a population variance of more than 0.015 square ounces, then it must me adjusted. Test at 1% significance level whether the machine needs to be adjusted.

Answer 1

Null hypothesis: variance is 0.015

 

 

S = (n-1)*s^2/ S^2 where s is the sample standard deviation and S is the population standard deviation

 

  = (25-1)*(0.029)^2 / (0.015)^2 = 89.706

 

 

The p -level threshold per the Chi Square table is 11.524 ( 1% significance with 25 degrees of freedom)

is 44.314

 

 

the test statistic shows are higher probability than the p -level

Accepts Null Hypothesis