An IQ test is designed so that the mean is 100 and the standard deviation is 23

Question

An IQ test is designed so that the mean is 100 and the standard deviation is 23 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 95 % confidence that the sample mean is within 4 IQ points of the true mean. Assume that sigma equals23 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 _____.

(Round up to the nearest integer.)

HOW DO YOU DO THIS ON THE TI- 84 Plus Silver Calculator?

Explanation / Answer

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  

[You can do this part using Invnorm(0.025, 0, 1), as this is a z distrbution. You will get a negative value though, just get the absolute value.]
      
Also,      
      
s = sample standard deviation =    23  
E = margin of error =    4  
      
Thus,      
      
n = (1.959963985)^2*(23^2)/(4^2) =   127.0082323  
      
Rounding up,      
      
n =    128   [ANSWER]

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Yes, it is practical, as it is easy to conduct 128 IQ tests.

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