3 pts Banana Republic is interested in knowing the proportio

(3 pts) Banana Republic is interested in knowing the proportion of adults who buy clothing online.

How many adults must be surveyed in order to be 95% confident that the sample proportion is within

3 percentage points (.03)? Show work, answer question, and give units

Solution

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.025  
As there is no previous estimate for p, we set p = 0.5.      
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
E =    0.03  
p =    0.5  
      
Thus,      
      
n =    1067.071895  
      
Rounding up,      
      
n =    1068 adults [ANSWER]