An IQ test is designed so that the mean is 100 and the standard deviation is 10

Question

An IQ test is designed so that the mean is 100 and the standard deviation is 10 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99% confidence that the sample mean is within 4 IQ points of the true mean. Assume that sigma =10 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

The required sample size is­________?

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 =    10  
E = margin of error =    4  
      
Thus,      
      
n =    41.46810376  
      
Rounding up,      
      
n =    42   [ANSWER]

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Yes, this is reasonable, because it is easy to invite 42 people to get an IQ test, and it is cheap.

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