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. 5 17 12 21 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. (Give the answer to two decimal places.)

Answer 1

[0.9 months, 32.69 months]

Explanation:

The mean is

`\bf \bar x=(5+17+12+21+29)/(5)=16.8`

The standard deviation is

`\bf s=\sqrt{((5-16.8)^2+(17-16.8)^2+(12-16.8)^2+(21-16.8)^2+(29-16.8)^2)/(5)}=8.1092`

Now, we have to find two values a and b such that the area under the Normal curve with mean 16.8 and standard deviation 8.1092 between a and b equals 95% = 0.95

Using a spreadsheet we find these values are

a = 0.906

b = 32.694

(See picture)

and our 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 rounded to two decimal places is

[0.9 months, 32.69 months]