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I am trying to understand how to apply the Binomial test to the following problem:

From the first box, we retrieved 10 rotten tomatoes, from the second none. Use the binomial test to test if rotten tomatoes is significantly more frequent in the first box.

In classical examples it is necessary to provide the probability of events and number of experiments. Two questions I have so far:

  1. do we have enough data;

  2. (in the case they are enough ...) how to apply Binomial test to find an answer?

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    $\begingroup$ You need to randomly select assuming both boxes contain a large number of tomatoes. Then you need to know $n_1$ the number of tomatoes drawn from the first box and $n_2$ the number of tomatoes drawn from the second box. $\endgroup$
    – Michael R. Chernick
    Commented Apr 24, 2017 at 21:11
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    $\begingroup$ Ok in our case we have a large number of tomatoes, $n_1 = 10$ and $n_2 = 0$. What should I do next? $\endgroup$
    – Jolly Jumper
    Commented Apr 24, 2017 at 21:21
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    $\begingroup$ If $n_2$ is 0 you can't say anything because you haven't sampled from the second box. You are confusing the sample sizes with the number of rotten tomatoes. Let $x_1$ represent the number of rotten tomatoes found in the sample from box 1 and $x_2$ the number found in the sample from box 2. In your case $x_1$=10 and $x_2$=0. Given that you counted how many good tomatoes were in each sample you would know $n_1$ and n$.2$. Given that information you can then do a two sample binomial test to conclude whether or not box 1 has more rotten tomatoes than box 2. $\endgroup$
    – Michael R. Chernick
    Commented Apr 24, 2017 at 21:31

1 Answer 1

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Let $X_1\sim \mathcal{Binom}(n_1, p_1), \quad X_2\sim\mathcal{Binom}(n_2, p_2)$. You observed $X_1=10, X_2=0$. You didn't tell us $n_1, n_2$.

Assuming you know $n_1, n_2$, you have enough data for a binomial test of $H_0\colon p_1=p_2$. How to do the test are discussed in multiple posts on this site:

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