A new medication designed to lower cholesterol is being test

A new medication designed to lower cholesterol is being tested. The drug is only considered to be effective if it lowers cholesterol by at least 20 points during a 3 month time period. The researchers want to form a 95% confidence interval for the true mean cholesterol reduction and want it to have a width no bigger than 1 point. They have a good idea, based on previous studies of drugs of this sort, that the population standard deviation is 3.52 points. Their sample should be at least how big?

a)7 b)15 c)50 d)191 e)234

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.025  
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
s = sample standard deviation =    3.52  
E = margin of error =    1  
      
Thus,      
      
n =    47.59721137  
      
Rounding up,      
      
n =    48 --> 50 [ANSWER, C]