Question

1. When we did hypothesis testing for proportions in class, we were able to use a normal distribution in all cases, provided the sample size was large enough. Explain why we can always apply the Central Limit Theorem to a random variable X, if X ∼ Bern(p) and the sample size is sufficiently large.

Answer 1

We know that,

In the statement of central limit theorem there is one condition as sample size should be sufficiently large, which is because as n tends to infinity sample proportion converges to population proportion. That means that, when sample size increases, the difference between the value of sample proportion and population proportion become smaller and smaller.

Hence, To apply central limit theorem, we should have sufficiently large sample size.

Thank you.