Assume that two independent random samples of sizes and have been selected from binomial populations with parameters and , respectively. The sampling distribution of can be approximated by a normal distribution provided that and are all greater than 5.

Question

Assume that two independent random samples of sizes  and  have been selected from binomial populations with parameters  and  , respectively. The sampling distribution of  can be approximated by a normal distribution provided that  and  are all greater than 5.

Quizplus · Accepted Answer

This statement follows the central limit theorem, which states that as sample size increases, the sampling distribution approaches a normal distribution. Additionally, the condition that both n*p and n*(1-p) are greater than 5 ensures that the binomial distribution is not too skewed, which also allows for the normal approximation.

Assume That Two Independent Random Samples of Sizes and