Question

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 1

A 95% confidence interval for the mean number of months elapsed since the last visit to a dentist, is
`[5.79063, 28.20937]`

Explanation:

We will build a 95% confidence interval for the mean number of months elapsed since the last visit to a dentist. A (1 -
`\alpha`) x100% confidence interval for the mean number of months elapsed since the last visit to a dentist with unknown variance and is given by:

`[\bar x -T_{(n-1,(\alpha)/(2))} (S)/(√(n)), \bar x +T_{(n-1,(\alpha)/(2))} (S)/(√(n))]`

`\bar X = 17`

`n = 5`

`\alpha = 0.05`

`T_{(n-1,(\alpha)/(2))}=2.7764`

`S = 9.0277`

`[17 -2.7764 (9.0277)/(√(5)), 17 +2.77644 (9.0277)/(√(5))]`

A 95% confidence interval for the mean number of months elapsed since the last visit to a dentist, is
`[5.79063, 28.20937]`