Is there more variation in the output of one shift in a manufacturing plant than

Question

Is there more variation in the output of one shift in a manufacturing plant than in another shift? In an effort to study this question, plant managers gathered productivity reports from the 8 a.m. to 4 p.m. shift for eight days. The reports indicated that the following numbers of units were produced on each day for this shift.

5528 4779 5112 5380 4918 4763 5055 5106

Productivity information was also gathered from seven days for the 4 p.m. to midnight shift, resulting in the following data.

4325 4016 4872 4559 3982 4754 4116
Use these data and a=0.01 to test to determine whether the variances of productivity for the two shifts are the same. Assume productivity is normally distributed in the population.

Explanation / Answer

n1=8, s1= 270.02 n2=7, s2=359.96 Given a=0.01, the F with 0.005, df1=n1-1=7, df2=n2-1=6 is 0.11 (check F table) F with 0.995, df1=7, df2-6 is 11.22 (check F table) The test hypothesis is Ho:s1^2=s2^2 Ha:s1^2 not equal to s2^2 The test statistic is F=s1^2/s2^2 =270.02^2/359....

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