In: Statistics and Probability
In a clinical trial, 50 patients who received a new medication are randomly selected. It was found that 10 of them suffered serious side effects from this new medication. Let p denote the population proportion of patients suffered serious side effects from this new medication.
Find the minimum sample size needed to estimate the population proportion p with 90% confidence such that the estimate is accurate within 0.04 of p.
sample proportion ,   p̂ =10/50 = 0.2  
           
           
sampling error ,    E =   0.04  
           
           
Confidence Level ,   CL=   0.90  
           
           
          
           
           
alpha =   1-CL =   0.10  
           
           
Z value =    Zα/2 =    1.645   [excel
formula =normsinv(α/2)]      
           
   
          
           
           
Sample Size,n = (Z / E)² * p̂ * (1-p̂) = (  
1.645   /   0.04   ) ² *  
0.20   * ( 1 -   0.20   ) =
   270.55
          
           
           
          
           
           
so,Sample Size required=      
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