An article gave the following summary information for fracture strengths (MPa) o

Question

An article gave the following summary information for fracture strengths (MPa) of n = 144 ceramic bars fired in a particular kiln: x = 61.35, s = 3.36. (a) Calculate a (two-sided) confidence interval for true average fracture strength using a confidence level of 95%. (Round your answers to two decimal places.) Does it appear that true average fracture strength has been precisely estimated? (b) Suppose the investigators had believed a priori that the population standard deviation was about 8 MPa. Based on this supposition, how large a sample would have been required to estimate mu to within 0.5 MPa with 95% confidence?

Explanation / Answer

b)

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 =    8  
E = margin of error =    0.5  
      
Thus,      
      
n =    983.4134581  
      
Rounding up,      
      
n =    984   [ANSWER]

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Hi! I think you just rounded down. Note that we should always round up when getting the sample size. [Like, 12.1 --> 13, that is.] Thanks!

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