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I am trying to solve the following exercise:

A control authority needs to test that the probability of getting $0$ at roulette is $1/37$ and bigger.

After 1000 trials, they get the number $0$ $40$ times.

I need to write a formula for the specific number of the p-value of this test and for a good approximation of it.

Now, I know that:

$$ \text{p-value} = sup_{\theta \in \theta_0} \mathbb{P}(W(X) > W_{observed} ) $$

Where W(X) is the statistics $W_{observed}$ is the value of the observed statistics.

In this case my test is : I refuse $H_0$ if the W(X) > $\frac{1}{37}$

However here I am stuck. I must say I am quite confused by this topic so please forgive me for any misunderstanding in the question.

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