8 The use of the internet is constantly growing How many ran

8. The use of the internet is constantly growing. How many randomly selected adults must be surveyed to estimate the percentage of adults in the United States who now use the internet? Assume we want to be 99% confident that the sample percentage is within 2 percentage points of the true population percentage. a) Assume that nothing is known about the percentage of adults using the internet. b) Assume it was estimated that 72% of adults in the United States use the internet.

Solution

A)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.005  
As there is no previous estimate for p, we set p = 0.5.      
      
Using a table/technology,      
      
z(alpha/2) =    2.575829304  
      
Also,      
      
E =    0.02  
p =    0.5  
      
Thus,      
      
n =    4146.810376  
      
Rounding up,      
      
n =    4147   [ANSWER]

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b)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.005  
       
      
Using a table/technology,      
      
z(alpha/2) =    2.575829304  
      
Also,      
      
E =    0.02  
p =    0.72  
      
Thus,      
      
n =    3343.987887  
      
Rounding up,      
      
n =    3344   [ANSWER]