A university dean is interested in determining the proportio

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 1% with 98% reliability, how many students would need to be sampled?

A. 5637

B. 132

13,088

3177

Solution

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.01  
       
      
Using a table/technology,      
      
z(alpha/2) =    2.326347874  
      
Also,      
      
E =    0.01  
p =    0.59  
      
Thus,      
      
n =    13091.37263  
      
Rounding up,      
      
n =    13092   [ANSWER, OPTION C]

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We choose the closest answer, as there coudl be some round off errors in the calculation of your instructor. Anyway, the other choices are far from this.