You randomly select a group of 100 UIC students to take your

You randomly select a group of 100 UIC students to take your survey, and 61 students fill it out. You calculate the average HOS scores to be mean=40.39, standard deviation=22.04. Give a 95% confidence interval for the HOS scores of all UIC students.

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 =    40.39          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    22.04          
n = sample size =    61          
              
Thus,              
Margin of Error E =    5.530886721          
Lower bound =    34.85911328          
Upper bound =    45.92088672          
              
Thus, the confidence interval is              
              
(   34.85911328   ,   45.92088672   ) [ANSWER]