Question

A recent study shows that 11% of all Americans have a graduate or professional degree. A sociologist takes a random sample of 500 people to begin a research project. With a 25% chance, the sociologist's sample proportion will be no greater than what value of p̂ ? Use Excel to find your answer and round it to the nearest hundredth."

Answer 1

We are given the proportion value here as p = 0.11 and the sample size as n = 500.

Therefore the distribution of the sample proportion would be given here as:

From standard normal tables, we are to find here:
P(Z < p) = 0.75

Using EXCEL, we get the value as:
=norm.inv(0.75,0,1)

0.6745 is the output here.

Therefore the value of p here is computed as:
= Mean + 0.6745*Std Dev
= 0.11 + 0.6745*0.0140
= 0.1194

Therefore with a 25% chance, the socialogist sample proportion will be no more than 0.1194.