Construct a confidence interval of the population proportion

Construct a confidence interval of the population proportion at the given level of confidence. x= 125, n=250, 99% confidence The 99% confidence interval is (_______, _________). (Use ascending order. Round to three decimal places as needed.)

Solution

Confidence Interval Estimate for the Proportion

Data

Sample Size

250

Number of Successes

125

Confidence Level

99%

Intermediate Calculations

Sample Proportion

0.5

Z Value

2.576

Standard Error of the Proportion=sqrt(0.5*0.5/250)=

0.0316

Interval Half Width=0.0316*2.576=

0.0814

Confidence Interval

Interval Lower Limit =(0.5-0.0814) =

0.4186

Interval Upper Limit =(0.5+0.0814) =

0.5814

Result: Confidence intervals =(0.419, 0.581)     ( three decimals)

Confidence Interval Estimate for the Proportion
Data
Sample Size	250
Number of Successes	125
Confidence Level	99%
Intermediate Calculations
Sample Proportion	0.5
Z Value	2.576
Standard Error of the Proportion=sqrt(0.5*0.5/250)=	0.0316
Interval Half Width=0.0316*2.576=	0.0814
Confidence Interval
Interval Lower Limit =(0.5-0.0814) =	0.4186
Interval Upper Limit =(0.5+0.0814) =	0.5814