PLEASE SHOW EACH AND EVERY STEP. THANK YOU!!! Is there more variation in the out
ID: 3231167 • Letter: P
Question
PLEASE SHOW EACH AND EVERY STEP. THANK YOU!!!
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 8:00a to 4:00p 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 4:00p to midnight shift, resulting in the following. 4325 4016 4872 4559 3982 4754 4116 Use these data and alpha = 0.05 to test whether the variances of productivity for the two shifts are the same. (adapted from [Black 2012])Explanation / Answer
Data:
n1 = 8
n2 = 7
s1^2 = 72909
s2^2 = 129569.5
Hypotheses:
Ho: 1^2 = 2^2
Ha: 1^2 2^2
Decision Rule:
= 0.05
Numerator DOF = 8 - 1 = 7
Denominator DOF = 7 - 1 = 6
Lower Critical F- score = 0.1954
Upper Critical F- score = 5.6955
Reject Ho if F < 0.195366 or F > 5.6955
Test Statistic:
F = s1^2 / s2^2 = 72909/129569.5 = 0.5627
p- value = 0.765555
Decision (in terms of the hypotheses):
Since 0.195366 < 0.5627 < 5.6955 we fail to reject Ho
Conclusion (in terms of the problem):
There is no sufficient evidence that the population variances are different