SOLUTION: We wish to estimate what percent of adult residents in a certain county are parents. Out of 100 adult residents sampled, 35 had kids. Based on this, construct a 99% confidence in

Algebra ->  Probability-and-statistics -> SOLUTION: We wish to estimate what percent of adult residents in a certain county are parents. Out of 100 adult residents sampled, 35 had kids. Based on this, construct a 99% confidence in      Log On


   

Question 1182841: We wish to estimate what percent of adult residents in a certain county are parents.
Out of 100 adult residents sampled, 35 had kids.
Based on this, construct a 99% confidence interval for the proportion p of adult
residents who are parents in this county.
Express the answer in tri-inequality.
Answer as decimals, to 3 places.
_________ < p < __________ Express the same answer using the point estimate and margin of error.
Answer as decimals, to 3 places
p̂±E = _________ ± _____________
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
On your TI-84,

press STAT
press the right arrow key twice to highlight TESTS
Scroll down to A:1-PropZInt
Press ENTER

Make the next screen read like this:

                      1-PropZInt
                  x:35
                  n:100
                  C-Level:0.99 
                  Calculate

Scroll down to highlight Calculate
Press ENTER

Read this:

                      1-PropZInt
                   (.22714,.47286) 
                   p̂=.35
                   n=100
        That means:

       0.22714 < p < 0.47286

Express the same answer using the point estimate and margin of error.
Notice that if you average the two boundaries of the interval you get point
estimator p̂:

p̂ = %280.22714%2B0.47286%29%2F2=0.7%2F2=0.35

The margin of error E is the absolute value difference between the point-
estimator, p̂, and either boundary:

E = |0.22714-0.35| = |0.47286-0.35| = 0.12286

p̂±E =  0.35 ± 0.12286

Edwin