Now carry out the same analysis, only instead of simulating the null, use the theory-based (normal approximation) approach for that null distribution. How does the p-value you found using the theory-based approach compare to the one you found using simulation

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis:

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