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

Assume the population distribution is normal and use that fact to create a 90% CI for µ.

Solution

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.05          
X = sample mean =    4.32          
t(alpha/2) = critical t for the confidence interval =    1.894578605          
s = sample standard deviation =    2.528816776          
n = sample size =    8          
df = n - 1 =    7          
Thus,              
              
Lower bound =    2.6261108          
Upper bound =    6.0138892          
              
Thus, the confidence interval is              
              
(   2.6261108   ,   6.0138892 ) [ANSWER]