Question

For a given population, the percentage of full-time employees that participate in a retirement plan is 67%. When a retirement specialist sets up a study, they are curious about the impact of sample size on the standard error. What is the standard error of the sampling distribution of sample proportions for samples of size n=200, n=400, and n=1,500?

Round all answers to the nearest hundredths if applicable.

Provide your answer below:

If $n=200$n=200​ then $\sigma_{p̂}$σp̂​​  =

If  $n=400$n=400​ then  $\sigma_{p̂}$σp̂​​ =

If  $n=1,500$n=1,500​ then  $\sigma_{p̂}$σp̂​​ =

Answer 1

1)
sample proportion, = 0.67
sample size, n = 200
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.67 * (1 - 0.67)/200) = 0.03

2)

sample proportion, = 0.67
sample size, n = 400
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.67 * (1 - 0.67)/400) = 0.02

3)

sample proportion, = 0.67
sample size, n = 1500
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.67 * (1 - 0.67)/1500) = 0.01