Question

5. Why are the requirements np >= 10 and nq >= 10 include in the central limit theorem for proportions? What role do they play in the theorem?

Answer 1

Solution: The requirements np >=10 and nq >= 10 are included in the central limit theorem for proportion because these requirements make sure the sample size is large and the probability of success is close to 0.5. The central limit theorem states that if a sufficiently large sample is drawn from a non-normal population, then the sampling distribution of sample proportions will follow the approximately normal distribution. Therefore, the conditions np > 10 and nq > 10 fulfill the requirement of a large sample.