for each of the following below sets of smaple outcomes use

for each of the following below sets of smaple outcomes use formula confidence interval sample porportion large samples Ps±Z(square root)^Pu(1-Pu)_/N construct the 99% confidence interval for estimating Pu

B. Ps= .37 N=522

C. Ps= .79 N=121

E. Ps= .43 N=1049

Solution

a)
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Sample Size(n)=522
Sample proportion = x/n =0.37
Confidence Interval = [ 0.37 ±Z a/2 ( Sqrt ( 0.37*0.63) /522)]
= [ 0.37 - 2.58* Sqrt(0.0004) , 0.37 + 2.58* Sqrt(0.0004) ]
= [ 0.3155,0.4245]

B)

Sample Size(n)=121
Sample proportion = x/n =0.79
Confidence Interval = [ 0.79 ±Z a/2 ( Sqrt ( 0.79*0.21) /121)]
= [ 0.79 - 2.58* Sqrt(0.0014) , 0.79 + 2.58* Sqrt(0.0014) ]
= [ 0.6945,0.8855]
c)
Sample Size(n)=1049
Sample proportion = x/n =0.43
Confidence Interval = [ 0.43 ±Z a/2 ( Sqrt ( 0.43*0.57) /1049)]
= [ 0.43 - 2.58* Sqrt(0.0002) , 0.43 + 2.58* Sqrt(0.0002) ]
= [ 0.3906,0.4694]