SOLUTION: If the standard error of the sampling distribution of the sample proportion is .0337 for samples of size 200, then the population proportion must be: ( A) 0.25 B

Algebra ->  Probability-and-statistics -> SOLUTION: If the standard error of the sampling distribution of the sample proportion is .0337 for samples of size 200, then the population proportion must be: ( A) 0.25 B      Log On


   

Question 161795: If the standard error of the sampling distribution of the sample proportion is .0337 for samples of size 200, then the population proportion must be: (
A) 0.25
B) 0.75
C) 0.20 or 0.80
D) 0.35 or 0.65

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for standard error is,
sqrt%28%28p%281-p%29%29%2Fn%29,
where p is the population proportion and n is sample size.
sqrt%28%28p%281-p%29%29%2Fn%29=sqrt%28%28p%281-p%29%29%2F200%29=.0337
%28p%281-p%29%29%2F200=.00113569
p%281-p%29=.227138
p-p%5E2=.227138
p%5E2-p%2B.227138=0
Use the quadratic formula,
p+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
p+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A%280.227138%29+%29%29%2F%282%2A1%29+
p+=+%281+%2B-+sqrt%28+1-4%2A1%2A%280.227138%29+%29%29%2F%282%2A1%29+
p+=+%281+%2B-+sqrt%28+1-.908522%29+%29%2F%282%29+
p+=+%281+%2B-+sqrt%28+.091448%29+%29%2F%282%29+
p+=+%281+%2B-+.3024+%29%2F%282%29+
.
.
.
p%5B1%5D+=+%281+%2B+.3024+%29%2F%282%29+
p%5B1%5D=1.3024%2F2=0.6512
.
.
.
p%5B2%5D+=+%281+-+.3024+%29%2F%282%29+
p%5B2%5D+=.6976%2F2=0.3488+
.
.
.
The answer is D) 0.35 or 0.65.