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I'm simplifying a research question that I have at work. Assuming I have 2 coins each with a different probability of head, let's call heads a success (p). Those are biased coins each with a different p, and I do not know the probability of success of each coin, but I do got a sample:

Coin 1 - 4 head 3 tails

Coin 2 - 3 head 1 tails

Now I will like to reject an hypothesis that - coin 1 p= 0.3 and coin 2 p = 0.5, how can I do that?

Or/And I will also like to not reject a different hypothesis (state that it is not very very unlikely that this sample came from this hypotheses) - coin 1 p=0.7 and coin 2 p=0.7 (Is it the same calculation just depend on the p value?).

Also if I am in the same situation with more than 2 coins (5 coins with different size of sample for each coin)

Any help will be great, even directions of where to search as I did not manage to understand if there is a name of the problem I presented, and if so what it is.

Thank you.

Coin 1 - 4 head 3 tails

Coin 2 - 3 head 1 tails

Now I will like to reject an hypothesis that - coin 1 p= 0.3 and coin 2 p = 0.5, how can I do that?

Or/And I will also like to not reject a different hypothesis (state that it is not very very unlikely that this sample came from this hypotheses) - coin 1 p=0.7 and coin 2 p=0.7 (Is it the same calculation just depend on the p value?).

**EDIT - I am actually more interested to say that I can not reject an hypothesis...**Also if I am in the same situation with more than 2 coins (5 coins with different size of sample for each coin)

Any help will be great, even directions of where to search as I did not manage to understand if there is a name of the problem I presented, and if so what it is.

Thank you.

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