Question

You are interested in finding a 90% confidence interval for the mean number of visits for physical therapy patients. The data below show the number of visits for 12 randomly selected physical therapy patients. Round answers to 3 decimal places where possible.

5

12

18

17

28

9

10

6

16

28

5

13

b. With 90% confidence the population mean number of visits per physical therapy patient is between  and   visits.

c. If many groups of 12 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About  percent of these confidence intervals will contain the true population mean number of visits per patient and about  percent will not contain the true population mean number of visits per patient.

Answer 1

b)
sample mean, xbar = 13.917
sample standard deviation, s = 7.937
sample size, n = 12
degrees of freedom, df = n - 1 = 11

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.796

ME = tc * s/sqrt(n)
ME = 1.796 * 7.937/sqrt(12)
ME = 4.115

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (13.917 - 1.796 * 7.937/sqrt(12) , 13.917 + 1.796 * 7.937/sqrt(12))
CI = (9.802 , 18.032)

With 90% confidence the population mean number of visits per physical therapy patient is between 9.802 and 18.032 visits.

c. If many groups of 12 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About 90 percent of these confidence intervals will contain the true population mean number of visits per patient and about 10 percent will not contain the true population mean number of visits per patient.