Question

Suppose we select a simple random sample of size n equals 325 from a large population with a proportion p of successes. let p hat be the proportion of successes in the sample. for which value of p is it appropriate to use the normal approximation for the sampling distribution of p hat

Answer 1

When selecting a simple random sample from a large population, it is appropriate to use the normal approximation for the sampling distribution of the sample proportion when both np and nq are greater than 5.

Step-by-step explanation:

When selecting a simple random sample from a large population, it is appropriate to use the normal approximation for the sampling distribution of the sample proportion (p hat) when both np and nq are greater than 5. Here, n represents the sample size and p represents the proportion of successes in the population.

For example, if we select a sample size of 325 (n = 325) and we want to estimate the proportion of successes in the population (p), we would need to ensure that both 325p > 5 and 325q > 5. If these conditions are met, we can approximate the sampling distribution of p hat using a normal distribution.