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How many samples are needed? (a)Given that, the required Confidence Level is 99%

ID: 3134705 • Letter: H

Question

How many samples are needed? (a)Given that, the required Confidence Level is 99%, Margin of Error is 3% and the assumed population proportion is 30%.(b)How many samples are needed? Given that, the required Confidence Level is 90%, Margin of Error is 2% and the assumed population proportion is 40%. (c)How many samples are needed? Given that, the required Confidence Level is 95%, Margin of Error is 3% and the population proportion is NOT available. (d)How many samples are needed? Given that, the required Confidence Level is 99%, Margin of Error is 2% and the population proportion is NOT available.

Explanation / Answer

A)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.005  
       
      
Using a table/technology,      
      
z(alpha/2) =    2.575829304  
      
Also,      
      
E =    0.03  
p =    0.3  
      
Thus,      
      
n =    1548.14254  
      
Rounding up,      
      
n =    1549   [ANSWER]

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b)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.05  
       
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
E =    0.02  
p =    0.4  
      
Thus,      
      
n =    1623.326072  
      
Rounding up,      
      
n =    1624   [ANSWER]

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c)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.025  
As there is no previous estimate for p, we set p = 0.5.      
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
E =    0.03  
p =    0.5  
      
Thus,      
      
n =    1067.071895  
      
Rounding up,      
      
n =    1068   [ANSWER]

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d)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.005  
As there is no previous estimate for p, we set p = 0.5.      
      
Using a table/technology,      
      
z(alpha/2) =    2.575829304  
      
Also,      
      
E =    0.03  
p =    0.5  
      
Thus,      
      
n =    1843.026834  
      
Rounding up,      
      
n =    1844   [ANSWER]

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