Question

According to a study of political​ prisoners, the mean duration of imprisonment for 33prisoners with chronic​ post-traumatic stress disorder​ (PTSD) was 33.3 months. Assuming that σ=40​months, determine a 90% confidence interval for the mean duration of​ imprisonment, μ​, of all political prisoners with chronic PTSD. Interpret your answer in words.

A 90% confidence interval for the population mean is from ___ months to___months

Interpret the confidence interval. Select the correct choice below and fill in the answer boxes to complete your choice.

​(Round to one decimal place as​ needed.)

A. We can be 90​% confident that the mean duration of​ imprisonment, μ​, of all political prisoners with chronic PTSD is somewhere between ___months and ___months.

or

B. There is a 90​% chance the mean duration of​ imprisonment, μ​, of all political prisoners with chronic PTSD will equal the mean of the interval from ___months to___months.

Answer 1

90% confidence interval for is

- Z * / sqrt(n) < < + Z * / sqrt(n)

33.3 - 1.645 * 40 / sqrt(33) < < 33.3 + 1.645 * 40 / sqrt(33)

21.8 < < 44.8

A 90% confidence interval for population mean is from 21.8 months to 44.8 months.

Interpretation -

We can be 90​% confident that the mean duration of​ imprisonment, , of all political prisoners

with chronic PTSD is somewhere between 21.8 months and 44.8 months.