Flossing helps prevent tooth decay and gum disease Yet repor

Flossing helps prevent tooth decay and gum disease. Yet reports suggest tht millions of Americans never floss.

You are planning a sample survey to determine what percent of students at your university never floss. you obtain permission to use the university roster to contact an SRS of students.

You want to estimate the proportion p of students who never floss with 98% confidence and a margin of error no greater than 4% (0.04).

Without relying on any previous knowledge, how large a sample do you need?

Hint: you can use the guess 0.50.

Solution

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.01  
As there is no previous estimate for p, we set p = 0.5.      
      
Using a table/technology,      
      
z(alpha/2) =    2.326347874  
      
Also,      
      
E =    0.04  
p =    0.5  
      
Thus,      
      
n =    845.6085049  
      
Rounding up,      
      
n =    846   [ANSWER]