Five students visiting the student health center for a free dental examination d

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 18 10 23 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.)

Explanation / Answer

Solution:

Let X be number of months had passed since their last visit for students to the dentist.

Xmean = (6 + 18 + 10 + 23 + 28)/5 = 17 months.

S^2(X) = (6^2 + 18^2 + 10^2 + 23^2 + 28^2 - 5*17^2)/4 = 82

P(17 - tst(3;0.975)*sqrt(82/5) < x < 17 + tst(3;0.975)*sqrt(82/5)) = 0.95

P(17 - 2.776*sqrt(82/5) < x < 17 + 2.776*sqrt(82/5)) = 0.95

P(17 - 11.2419 < x < 17 + 11.2419) = 0.95

P(5.7581 < x < 28.2419) = 0.95

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