Problem 2. Please show all steps and equations used. Thanks! a. To compare mean
ID: 3229737 • Letter: P
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Problem 2. Please show all steps and equations used. Thanks!
a. To compare mean performance of the two vendors, first compare variances to determine which t test to use. b. Based on part a, compare mean performance with the appropriate t test. 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 = 0.01 to test whether the variances of productivity for the two shifts are the same. (adapted from [Black 2012]) You're looking into two manufacturers (A and B) from which to purchase a large number of paving slabs for a large-scale construction project. You may use one manufacturer as a backup if necessary, but only if there's no significant difference in the weights of their paving slab.Explanation / Answer
Data:
n1 = 8
n2 = 7
s1^2 = 72909
s2^2 = 129569.5
Hypotheses:
Ho: 1^2 = 2^2
Ha: 11^2 2^2
Decision Rule:
= 0.01
Numerator DOF = 8 - 1 = 7
Denominator DOF = 7 - 1 = 6
Lower Critical F- score = 0.1092
Upper Critical F- score = 10.786
Reject Ho if F < 0.109226 or F > 10.786
Test Statistic:
F = s1^2 / s2^2 = 72909/129569.5 = 0.5627
p- value = 0.765555
Decision (in terms of the hypotheses):
Since 0.109226 < 0.5627 < 10.786 we fail to reject Ho
Conclusion (in terms of the problem):
There is no sufficient evidence that the population variances are different.
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