Question

12 independent random samples are collected from each of two silver plating companies. The samples yield standard deviations of S1= 0.035 mil and S2 = 0.062 mil. Do the data support, with 95% confidence, the contention that the plating done by Company 1 is less variable than that done by Company 2?

Answer 1

To Test :-

H0 :-

H1 :-

Test Statistic :-

f = 0.0012 / 0.0038
f = 0.3158

Test Criteria :-
Reject null hypothesis if f < f(1 - α , n1-1 , n2-1 )
f(1 - 0.05, 11 , 11 ) = 0.3549
f < f(1 - 0.05 , n1-1 , n2-1 ) = 0.3158 < 0.3549 , hence we reject the null hypothesis
Conclusion :- We Reject H0

Decision based on P value
P value = P ( f > 0.3158 ) = 0.0343
Reject null hypothesis if P value < α = 0.05
Since P value = 0.0343 < 0.05, hence we reject the null hypothesis
Conclusion :- We Reject H0

There is sufficient evidence to support the claim that Company 1 is less variable than that done by Company 2.