Consider the following data that represents a random sample

Consider the following data that represents a random sample out of a very large population:
0.43, 4.89, 5.29, 5.16, 0.59, 7.50, 4.48, 6.22

Regardless of your answer to (a), assume the population distribution is normal and use that fact to
create a 90% CI for µ.

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 =    0.05          
X = sample mean =    4.32          
z(alpha/2) = critical z for the confidence interval =    1.644853627          
s = sample standard deviation =    2.528816776          
n = sample size =    8          
              
Thus,              
              
Lower bound =    2.849382847          
Upper bound =    5.790617153          
              
Thus, the confidence interval is              
              
(   2.849382847   ,   5.790617153   ) [ANSWER]