Question

If nothing is known about​ p, 0.5 can be substituted for p in the​ sample-size formula for a population proportion. But when this is​ done, the resulting sample size may be larger than needed. Under what circumstances will using pequals0.5 in the​ sample-size formula yield a sample size larger than needed to construct a confidence interval for p with a specified bound and a specified confidence​ level?

Answer 1

ANSWER:

Whenever p is not the same as 0.5

(Whenever p is different from 0.5)

Step-by-step Explanation:

Recall that the sample size needed will be at it's maximum when p is equal to 0.5.​

Therefore, if p is equal to 0.5, i.e p=0.5 The​ sample size formula will yield the required sample size but whenever p is different from​ 0.5, using p=0.5 The​ sample size formula will yield a sample size larger than required to construct a confidence interval for p with a specified bound and a specified confidence level.