Question

An investigator takes a random sample of n people from a certain population to obtain the proportion p (hitherto unknown to the researcher) of smokers. Calculate the sample size you should take to ensure that the proportion of smokers does not differ from the true p-value by more than 0.01 with a probability of at least 0.95 using:

b) Central limit theorem

Answer 1

ANSWER:

b)

sample proportion ,   p̂ =    0.5                          
sampling error ,    E =   0.01                          
Confidence Level ,   CL=   0.95                          
                                  
alpha =   1-CL =   0.05                          
Z value =    Zα/2 =    1.960   [excel formula =normsinv(α/2)]                      
                                  
Sample Size,n = (Z / E)² * p̂ * (1-p̂) = (   1.960   /   0.01   ) ² *   0.50   * ( 1 -   0.50   ) =    9603.6
                                  
                                  
so,Sample Size required=       9604      

Sample size for a is greater than b

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