Question

1. What sample size is required to achieve a ME of ±4% at 90% confidence with an estimatedp = 0.3? Show how you arrived at your solution for full credit.

2. If a sample proportion is unknown, what sample size is required to achieve a ME of ±2% at 98% confidence ? Show how you arrived at your solution for full credit.

Answer 1

1. Sample proportion, p =    0.3      
Margin of error, E =+/- 4% = 0.04      
Significance level, α = 1- 0.90 = 0.10   
Critical value, z = NORM.S.INV( 0.10/2) = 1.645
          
Sample size, n =    (z² * p * (1-p)) / E²      

= 1.645² * 0.3 * 0.7 / 0.04²

= 355.1026 = 355

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2. if sample proportion is unknown we assume it to be 0.5

Sample proportion, p =    0.5      
Margin of error, E =    0.02      
Significance level, α = 1- 0.98 =  0.02      
Critical value, z = NORM.S.INV(   0.02   /2) =    2.3263
          
Sample size, n =    (z² * p * (1-p)) / E²      

= 2.3263² * 0.5 * 0.5 / 0.02²

=   3382.4340      

= 3382