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.) ( Incorrect: Your answer is incorrect. , Incorrect: Your answer is incorrect. ) You may need to use the appropriate table in Appendix A to answer this question. Need Help? Read It Chat About It

Solution

Given that 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.

The observations are 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.

Here sample size is small so we used here t - test.

A 95% Confidence interval for mean is,

Xbar - E < mu < Xbar + E

where Xbar is mean of observations.

E is the margin of error.

E = tc * s / sqrt(n)

s = standard deviation of data.

Xbar = sum of observations / total number of observations

Xbar = 86 / 5 =17.20

s = 1/n-1 (x - Xbar)²

s = 8.47

n = number of observations = 5

critical value = tinv(probability,d.f.)

probability = 0.05(alpha)

d.f. = n-1 = 4

critical value = 2.78

E = (2.78 * 8.47) / sqrt(5) = 10.51

lower limit = Xbar - E = 17.20 - 10.51 = 6.69

upper limit = Xbar + E = 17.2+10.51 = 27.71

95% CI for mean is (6.69 , 27.71)