Question

Last year, the percentage of baseball players that are drafted to play professional baseball was 9.5%. A sports reporter is writing an article about the chances of going pro and would like to back up their article with statistical analysis. If the reporter conducts a study, what is the standard error of the sampling distribution of sample proportions for samples of size n=50, n=100, and n=200?

Round all answers to the nearest thousandths if applicable.

Provide your answer below:

If $n=50$n=50​ then $\sigma_{p̂}$σp̂​​  =

If  $n=100$n=100​ then  $\sigma_{p̂}$σp̂​​ =

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

Answer 1

We have p = 9.5% = 0.095

1) if n = 50 ,

p^ = sqrt [ p*(1-p)/n] = sqrt [0.095*0.905/50]

p^ = 0.041

2) iff = 100

  p^ = sqrt [0.095*0.905/100] = 0.029

3) if n = 200

p^ = Sqrt [ 0.095*0.905/200]

p^ = 0.021