Hi, Please suggest a method to answer below questions:


Factory_ID   Factory_Location   Factory_Size       Total_Sample
Good_Sample   Fair_Sample   Bad_Sample
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

1                  City_A                      Big
100                      90                        10                 10
2                  City_A                      Big
120                     55                        35                 30
3                  City_A                      Small
80                      40                         25                15

4                  City_A                      Small
75                      50                         15                10
5                  City_B                      Big
150                      80                         30                40
6                  City_B                      Big
120                      55                         25                40
7                  City_B                      Big
125                      40                         80                  5
8                  City_B                      Big
100                     60                         25                15
9                  City_B                      Small
70                       45                         15                 10
10                City_B                      Small
85                       65                           5                 15
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

(1) Is there a statistically significant different between City_A and City_B
for the amount of Good_Quality_Sample that they produce?
(2) Is there a statistically significant different between Big and Small
factories for the amount of Good_Quality_Sample that they produce?

I don't think that t-test works here because the Total_Sample (i.e., the
total number of samples) from each factories is different.
I don't like to pool data from individual factory together. For example, I
don't like to pool Factory 1 and 2 together, because the variance among
individual Factory can be quite big in real data.


Thank you

Xiang

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