Question

We wish to estimate what percent of adult residents in a certain county are parents. Out of 600 adult residents sampled, 276 had kids. Based on this, construct a 99% confidence interval for the proportion, p, of adult residents who are parents in this county. Give your answers as decimals, to three places.

Answer 1

Level of Significance,   α =    0.01  
Number of Items of Interest,   x =   276  
Sample Size,   n =    600  
          
Sample Proportion ,    p̂ = x/n =    0.460

z -value =   "Zα/2 = 2.5758   [excel formula =NORMSINV(α/2)]

Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0203  
          
margin of error ,    E = Z*SE =    0.0524  
          
Confidence Interval          
Interval Lower Limit , =    p̂ - E =    0.408  
Interval Upper Limit , =    p̂ + E =   0.512  

confidence interval : 0.408<p<0.512