A psychologist is studying the self image of smokers, which she measures by the

Question

A psychologist is studying the self image of smokers, which she measures by the self-image (SI) score from a personality inventory. She would like to estimate the mean SI score, m , for the population of all smokers. She plans to take a random sample of SI scores for smokers and estimate m via this sample. Assuming that the standard deviation of SI scores for the population of all smokers is 80, what is the minimum sample size needed for the psychologist to be 99% confident that her estimate is within 15 ofm ? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).

Explanation / Answer

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.005  
      
Using a table/technology,      
      
z(alpha/2) =    2.575829304  
      
Also,      
      
s = sample standard deviation =    80  
E = margin of error =    15  
      
Thus,      
      
n =    188.7259478  
      
Rounding up,      
      
n =    189   [ANSWER]

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