Question

e Hypothesis Tests for Variances and Proportions in Six Sigma Case Study A Six Sigma team at a factory that produces dog biscuits is charged with reducing the amount of variation in the weight of filled boxes of product. To accomplish this, the team is considering replacing the old packing machine with a new one. A sample of ten boxes filled by the old machine displays a variation of 1.70. A similar sample from the new machine yields a variation of 0.52 Answer the questions in order Question 1 Question 2

Answer 1

Answer : A six Sigma team at a factory tht produces dog biscuits is chrged with reducing the amount of variation in the weight of filled boxes of product to accomplish this the team is considering replacing the old packing machine with a new one. A sample of 10 boxes filled by the old machine displays a variation of 1.70 a similar sample from the new machine yields a variation of 0.52.

Solution :

F- statistic :

the old machine displays a variation of 1.70

S1^2 = 1.70

the new machine yields a variation of 0.52.

S2^2 = 0.52

Therefore,

F-Statistic = S1^2 / S2^2

                   = 1.70 / 0.52

                   = 3.269

   F Statistic = 3.27

At α = 0.05, from F distribution table

Degree of freedom (numerator) = 10 - 1

                                                         =9

Degree of freedom (denominator) = 10 - 1

                                                              = 9

Therefore,

Critical value for F-distribution,

CV = F( 9, 9,at 0.05)

      = 3.18.      (From F-distribution table).

Therefore,

F- statistic = 3.27

Critical value = 3.18