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.

## Best Answer

No, it is not correct. In this example you have

two samplesso 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.