According to an article in US News and World Report (April 12, 1999), the Natura

Question

According to an article in US News and World Report (April 12, 1999), the Natural Resources Defense Council (NRDC) warned that bottled water may contained more bacteria and other potentially carcinogenic chemicals than allowed by state and federal regulations. Of the more than 1000 bottles studied, approximately one-third exceeded government levels. Suppose that NRDC wants an updated estimate of the population proportion of bottled water that violates at least one governmental standard. Determine the sample size needed to estimate this proportion using a 95% confidence interval with a width of 0.03.

Explanation / Answer

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 =    0.03  
p = 1/3 =   0.333333333  
      
Thus,      
      
n =    948.5083508  
      
Rounding up,      
      
n =    949   [ANSWER]

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