Question

If the population proportion is p=0.60, will the shape of the sampling distribution of p^ predicted for random samples of size 100 be approximately Normal?

Answer 1

The shape of the sampling distribution of p^ predicted for random samples of size 100 will be approximately Normal if the conditions np > 5 and nq > 5 are met.

Step-by-step explanation:

When you perform a hypothesis test of a single population proportion p, you take a simple random sample from the population. The shape of the binomial distribution needs to be similar to the shape of the normal distribution. To ensure this, the quantities np and nq must both be greater than five (np > 5 and nq > 5). Then the binomial distribution of a sample pq (estimated) proportion can be approximated by the normal distribution with μ = p and σ = √((pq)/n).