How to Test for Equality of Selective First Items from Three Factories?

[dumbest]

first of all , hello everyone

you can see who i am depending on my nickname ,

but i need your help

i have one question :" Three factory creates the same item ,

from the first factory is selected 250 item and 10 of them is defective
from the second factory 200 and 9 of them is defective
from the third 150 and 11 of them is defective

a=0.1 ( Alpha = 0.1 )
question is : test hypothesis about equality of these "selections" ( i don`t know how to say exactly ) "should i test the first two of them using " Two-proportion z-test " and then test one of them and third using again " Two-proportion z-test " ... ?anyone ?

 

[EnumaElish]

You can test them in pairs, with the caveat that pairwise tests are not transitive: if x = y and y = z are both statistically significant, it does not follow that x = z is also stat. significant. In your case, they may turn out to be consistent; I haven't tried.

The alternative is to use ANOVA for three Binomial distributions. You can estimate within-group (sample) variances using the binomial variance formula n_jp_j(1-p_j) for the j'th group, then set it equal to the sample variance, s_n² (substitute n_j for n) then solve for the sum of squared deviations from the mean for the j'th sample (j = 1, 2, 3).

 

[dumbest]

thanks for an answer ,

i think they must be consistent ,

because the alternative way ( anova ... ) will take more time and that way is not defined by teacher yet ...

students do not know what is Anova ... sorry for my bad english and thanks for an answer ...

 

[EnumaElish]

Please post homework questions in the homework forums.