Estimating Population Parameters with Error Margin Practice Test

A park district wants to estimate the population parameter $p$, the proportion of all residents who visited a park in the last month. A random sample of $n=150$ residents found a sample statistic $\hat{p}=0.48$ (48%). Students used simulation/repeated sampling and reported: in 1,000 simulated samples of size 150, about 95% of the simulated sample proportions were within 0.05 of 0.48.

Which interval is a reasonable estimate range for the population parameter $p$? (Give the interval in decimals.)

A store wants to estimate the population parameter $p$, the proportion of all customers who use self-checkout. A random sample of 500 customers found 310 used self-checkout, so the sample statistic is $\hat p = 310/500 = 0.62$ (62%). Students ran a simulation of 1,000 repeated random samples of size 500 and found that about 95% of simulated sample proportions were between 0.58 and 0.66.

What margin of error is supported by the simulation for estimating the population parameter $p$? (Express your answer as a percent.)