A corona group warts to estimate the mean electric bill for

A. corona group warts to estimate the mean electric bill for the month of May for single family homes m a large city Based on studies conducted for other cities, the standard dcwi&oti; is assumed to be $ 35. The group warts to estimate with 99% confidence. the mean bd for May to within plusminus $7 What sample size is needed

Solution

a)

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.005  
      
Using a table/technology,      
      
z(alpha/2) =    2.575829304  
      
Also,      
      
s = sample standard deviation =    35  
E = margin of error =    7  
      
Thus,      
      
n =    165.872415  
      
Rounding up,      
      
n =    166   [ANSWER]

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b)

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.025  
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
s = sample standard deviation =    35  
E = margin of error =    7  
      
Thus,      
      
n =    96.03647052  
      
Rounding up,      
      
n =    97   [ANSWER]