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 17 11 22 29 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.

Answer:A 95% confidence interval for the mean number of months elapsed since the last visit to a dentist, is [tex][5.79063, 28.20937][/tex]Step-by-step explanation:We will build a 95% confidence interval for the mean number of months elapsed since the last visit to a dentist. A (1 - [tex] \alpha [/tex]) x100% confidence interval for the mean number of months elapsed since the last visit to a dentist with unknown variance and is given by:[tex][\bar x -T_{(n-1,\frac{\alpha}{2})} \frac{S}{\sqrt{n}}, \bar x +T_{(n-1,\frac{\alpha}{2})} \frac{S}{\sqrt{n}}][/tex][tex]\bar X = 17[/tex][tex]n = 5[/tex][tex]\alpha = 0.05[/tex][tex]T_{(n-1,\frac{\alpha}{2})}=2.7764[/tex][tex]S = 9.0277[/tex][tex][17 -2.7764 \frac{9.0277}{\sqrt{5}}, 17 +2.77644 \frac{9.0277}{\sqrt{5}}][/tex]A 95% confidence interval for the mean number of months elapsed since the last visit to a dentist, is    [tex][5.79063, 28.20937][/tex]