Suppose that 30 samples are taken from a normally distribute

Suppose that 30 samples are taken from a normally distributed population with an unspecified mean mu and a variance sigma^2 = 1. Below are the 30 samples: Construct a 95% confidence interval for mu based on the above information.

Solution

Note that              
              
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 =    10.7          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    1          
n = sample size =    30          
              
Thus,              
              
Lower bound =    10.34216117          
Upper bound =    11.05783883          
              
Thus, the confidence interval is              
              
(   10.34216117   ,   11.05783883   ) [ANSWER]