Five students visiting the student health center for a free

Five students visiting the student health center for a free dental examination during National Dental Hygiene Month were asked how many months had passed since their last visit to a dentist. Their responses were as follows. 6 19 12 21 28

Assuming that these five students can be considered a random sample of all students participating in the free checkup program, construct a 95% confidence interval for the mean number of months elapsed since the last visit to a dentist for the population of students participating in the program. (Give the answer to two decimal places.)

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 =    0.025          
X = sample mean =    16.4          
t(alpha/2) = critical t for the confidence interval =    2.776445105          
s = sample standard deviation =    8.820430828          
n = sample size =    5          
df = n - 1 =    4          
Thus,              
              
Lower bound =    5.447988592          
Upper bound =    27.35201141          
              
Thus, the confidence interval is              
              
(   5.45 ,   27.35 ) [ANSWER]