A sample of size n 100 produced the sample mean of X 16 As

A sample of size n = 100 produced the sample mean of X = 16. Assuming the population standard deviation o = 3, compute a 95% confidence interval for the population mean µ.

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Solution

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    16          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    3          
n = sample size =    100          
              
Thus,              
Margin of Error E =    0.587989195          
Lower bound =    15.4120108          
Upper bound =    16.5879892          
              
Thus, the confidence interval is              
              
(   15.4120108   ,   16.5879892   ) [ANSWER]