Executives of a supermarket chain are interested in the amount of time that cust

Question

Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time, mu, of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate mu. Assuming that the standard deviation of the population of shopping times at the supermarkets is 26 minutes, what is the minimum sample size she must collect in order for her to be 99% confident that her estimate is within 3 minutes of mu ? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.)

Explanation / Answer

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 =    26  
E = margin of error =    3  
      
Thus,      
      
n =    498.3544558  
      
Rounding up,      
      
n =    499   [ANSWER]

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