Calculating p values and degree of freedom
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Introduction
We calculating P value of populations with different variances
n1=62
n2=62
F-Calculated =2(current)/2(proposed)
Mean (current) = (76+76+77+…………. +66+70+74+72)/62=4579/62
=75.06557377
Mean (proposed) = (74+75+77+…………. +74+72+78+71)/62=4601/62
=75.42622951
Variance=1/n∑ x2-n (x‾)
1/62{(76*76+76*76+77*77+…………. +66*66+70*70+74*74+72*72)-62(75.06557377)
=15.56229508
Variance (proposed) =1/62{74*74+75*75+77*77+………+74*74+72*72+78*78+71*71)-62(75.42622951)
=6.281967213
F-calculated= 15.56229508/6.281967213
=2.477296
Degree of freedom
(N1-1, n2-1)= (61, 61)
CRITICAL F-VALUE (61, 61) at α=0.05
=1.52883315
Since F-calculated=2.477 is greater than F (61, 61) reject the null hypothesis.
Conclusion
There is sufficient evidence at α=0.05 level to conclude that the average change driven by current state of the machinery differs from average speed driven by proposed machinery.
References
Hedgecock, D., Chow, V., & Waples, R. S. (2012). Effective population numbers of shellfish broodstocks estimated from temporal variance in allelic frequencies. Aquaculture, 108(3-4), 215-232.