Question

A psychiatrist is interested in finding a 90% 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.

6

3

0

9

6

0

7

3

2

4

7

a. To compute the confidence interval use a ? t or z  distribution. _____

b. With 90% 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.

*** Enter an integral or decimal number, accurate to at least 4 decimal places.

Answer 1

a). from the given data n-11 which is less than 30 (small sample) Since the given data is small sample, To compute the confidence interval we use t-distribution From the given data Mean 4.272727 Standard deviation 2.969542 Formula for the 100(1-α)% confidence interval for population mean is, e,n-1) sd) ; we have α-0. land nll the 90% confidence interval for population mean is given by. C1-(i Therefore 2.969542 Cl = (4.272727 ± t(0.1.10)-11 from t-distributions t(0.1,10) (4.272727 1.622788) CI- (2.6499,5.8955) c). 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 90 percent of these confidence intervals will contain the true population mean number of tics per hour and about 10 percent will not contain the true population mean number of tics per hour.