626 Sample size requirements How large a sample is needed to

6.26 Sample size requirements. How large a sample is needed to estimate the incidence of female breast cancer in a population with 95% confidence and a margin of error that is no greater than 1% (0.01)? Assume that the expected incidence proportion in the population is 3% (0.03). How large a sample would be needed if you were willing to settle for 90% confidence? What was the effect of decreasing the required level of confidence?

Solution

a)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.025  
       
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
E =    0.01  
p =    0.03  
      
Thus,      
      
n =    1117.864517  
      
Rounding up,      
      
n =    1118   [ANSWER]

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b)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.05  
       
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
E =    0.01  
p =    0.03  
      
Thus,      
      
n =    787.3131451  
      
Rounding up,      
      
n =    788   [answer]

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As we can see, decreasing the level of confidence made the minimum sample size decrease as well. [ANSWER]