Question

A psychiatrist is interested in finding a 95% confidence interval for the tics per hour exhibited by children with Tourette syndrome. The data below show the tics in an observed hour for 11 randomly selected children with Tourette syndrome. Round answers to 3 decimal places where possible.

8

6

0

2

9

2

12

1

0

10

1

a. To compute the confidence interval use a

distribution.

b. With 95% confidence the population mean number of tics per hour that children with Tourette syndrome exhibit is between and .

c. If many groups of 11 randomly selected children with Tourette syndrome are observed, 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 tics per hour and about percent will not contain the true population mean number of tics per hour.

Answer 1

a)
t-distribution

b)

sample mean, xbar = 4.636
sample standard deviation, s = 4.456
sample size, n = 11
degrees of freedom, df = n - 1 = 10

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.228

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (4.636 - 2.228 * 4.456/sqrt(11) , 4.636 + 2.228 * 4.456/sqrt(11))
CI = (1.643 , 7.629)

c)
If many groups of 11 randomly selected children with Tourette syndrome are observed, then a different confidence interval would be produced from each group. About 95 percent of these confidence intervals will contain the true population mean number of tics per hour and about 5 percent will not contain the true population mean number of tics per hour.