Statistics Find Sample Size for Confidence Interval Thanks

Statistics - Find Sample Size for Confidence Interval

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Assume that the tips customers give to pizza delivery drivers follows a normal distribution with sigma = $0.74. Find the sample size necessary to produce a 98% confidence interval for n, the true mean tip given to pizza delivery drivers, of length 0 7.

Solution

Note that

margin of error = (length of interval/2) = 0.7/2 = 0.35.

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.01  
      
Using a table/technology,      
      
z(alpha/2) =    2.326347874  
      
Also,      
      
s = sample standard deviation =    0.74  
E = margin of error =    0.35  
      
Thus,      
      
n =    24.19227258  
      
Rounding up,      
      
n =    25   [ANSWER]