Setting null hypothesis for Binomial test I have a question for setting null hypothesis in binomial test.
More specifically, is there any way to assume chance level when it is unknown?
For example, let's say that I have a slightly bent coin. So chance for getting Heads or tails is not equal. Instead, it's more likely that it will give us tail.
To find out the probability, I tossed the coin 100 times, and got P(getting tail) = 68%
Then I bent it even more, and I wanted to check if it had any effect on the probability.
So I threw it 10 times and got tails 9 times (90%).
Is it correct to use one sample binomial test to check if 9 out of 10 (90%) is significantly different using 68% as expected probability?
I'm not sure if it's okay because it "assumes" that chance level is 68% based on experience of throwing the coin 100 times, instead of mathematical calculation.
Thanks for reading.

No, it is not correct.  In this example you have two samples so you should be using a two-sample hypothesis test.  There are a few different two-sample binomial tests available, so you will need to choose one.
