a soccer ball manufacturer wants to estimate the mean circum

a soccer ball manufacturer wants to estimate the mean circumference of soccer balls within o.i in.

a] determine the minimum sample size required to construct a 90% confidence interval for the population mean. assume the population standard deviation is 0.20in

b] repeat part a] using a standard deviation of 0.35in. which standard deviation requires larger sample size. Explain.

a] the minimum sample size required to construct a 90% confidence interval using standard deviation of 0.20in is -----balls

b] the minimum sample size required to construct a 90% confidence interval using a standard deviation of 0.35in is ------balls.

a population standard deviation of ----in requires a larger sample size. due to the increased variability in the population, a ----- sample size is needed to ensure the desired accuracy.

Solution

a)

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.05  
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
s = sample standard deviation =    0.2  
E = margin of error =    0.1  
      
Thus,      
      
n =    10.82217382  
      
Rounding up,      
      
n =    11   [ANSWER]

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b)

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.05  
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
s = sample standard deviation =    0.35  
E = margin of error =    0.1  
      
Thus,      
      
n =    33.14290731  
      
Rounding up,      
      
n =    34   [ANSWER]

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c)

a population standard deviation of 0.35 requires a larger sample size. due to the increased variability in the population, a GREATER sample size is needed to ensure the desired accuracy.