A group of 49 randomly selected students has a mean age of 2

A group of 49 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8 Construct a 98 Percentage confidence interval for the population mean.

Solution

8.

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 =    0.01          
X = sample mean =    22.4          
z(alpha/2) = critical z for the confidence interval =    2.326347874          
s = sample standard deviation =    3.8          
n = sample size =    49          
              
Thus,              
Margin of Error E =    1.26287456          
Lower bound =    21.13712544          
Upper bound =    23.66287456          
              
Thus, the confidence interval is              
              
(   21.13712544   ,   23.66287456   ) [ANSWER]