The sales manager for a hardware wholesaler finds that 229 o

The sales manager for a hardware wholesaler finds that 229 of the previous 500 calls to hardware store owners resulted in new product placements. Assume these 500 calls represent a random sample.

What is the upper confidence limit of a 95% confidence interval for the population proportion of new product placements?

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.458          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.022281652          
              
Now, for the critical z,              
alpha =   0.05          
Thus, z(alpha) =    1.644853627          

Thus,              
              
      
upper bound = p^ + z(alpha) * sp =    0.494650056   [ANSWER]