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The scenario is that a group of $n$ people carry out this same experiment.

Each person generates 11 random numbers based on the normal distribution $\mu=2.7$ and $\sigma=0.6$.

Each person must then calculate their own test statistic for the hypothesis:

$$H_0:\mu=2.7$$$$H_1:\mu\neq2.7$$

When I carried out this test using Excel, my test statistic was $-3.19$ which is less than the critical value at a 5% significance level ($-1.96$). Therefore I would reject the null hypothesis. However, this is only my experiment, how would I then calculate the proportion of the group I would expect to reject $H_0$?

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Denote the probability of rejecting the null hypothesis in one of the trials as P(Reject) (based on the normal distribution stated with 11 random numbers).

With N researchers the expected number that rejects is now a binomially distributed variable, so the fraction equals the probability of rejecting.

So by finding the probability that a researcher rejects the null, you find the fraction.

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In your case we know that the null hypothesis is always true.

Because you are using a 5% significance level, we know that you will reject the null hypothesis 5% of the times.

Using a binomial distribution with $p=0.05$ and $n=\text{number of people}$ you can easily compute the expected number of people that will reject $H_0$.

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