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:

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.

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)