5 10 choosing sample size Suppose you wish to estimate the m

5. [10] (choosing sample size) Suppose you wish to estimate the mean pH of rainfalls in an area that suffers heavy pollution due to the discharge of smoke from a power plant. Previous studies showed that the standard deviation is in the neighborhood of 0.4 pH, and you wish your estimate to lie within 0.1 of the unknown mean , with probability 0.90. Approximately how many rainfalls must be included in your sample?

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.05  
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
s = sample standard deviation =    0.4  
E = margin of error =    0.1  
      
Thus,      
      
n =    43.28869527  
      
Rounding up,      
      
n =    44   [ANSWER]