Suppose that each observation in a sample costs 10 to collec

Suppose that each observation in a sample costs $10 to collect and you have a budget of $1,500. Suppose that the population standard deviation of the measurement of interest is = 14. If you wish to estimate the population mean measurement with a 90% confidence interval with a margin of error of no more than 2.5, do you have sufficient money to collect a sample of the needed size? Justify your answer

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 =    14  
E = margin of error =    2.5  
      
Thus,      
      
n =    84.84584272  
      
Rounding up,      
      
n =    85  

Thus, the total cost is 85*$10 = $850.

As you have $1500, you have sufficient money. [ANSWER]