Question

A simulation was run 150 times with a population proportion of 0.70 and a simulated sample size of 50. The simulated sample proportion are shown below. Based on this distribution, what is the probability of obtaining a sample size of 50 with a sample proportion less than 0.60?

Answer 1

From the proportionality graph shown in the figure, the number of proportions less than 0.6 is:

$3+4+1+1=9$

The total number of simulations that were run is 150

Hence the probability of getting a sample proportion less than 0.6 is given by:

$P(p<0.6)=\frac{9}{150}\approx0.06$

Hence the probability is 0.06 or 6%.