This question is incomplete, the complete question is;
According to a study of political prisoners, the mean duration of imprisonment for 33 prisoners with chronic post-traumatic stress disorder (PTSD) was 34.2 months. Assuming that σ = 40 months.
determine a 95% confidence interval for the mean duration of imprisonment, μ , of all political prisoners with chronic PTSD. Interpret your answer in words.
Answer:
⇒ ( 20.6, 47.8 )
Therefore, 95% confidence interval for the mean duration of imprisonment μ of all political prisoners with PTSD is between 20.6 months and 47.8 months.
Explanation:
Given the data in the question;
sample size; n = 33
standard deviation σ = 40 months
x' = 34.2 months
Now, at 95% confidence interval;
we know that z-value of 95% confidence interval is 1.96
so we substitute into the formula below;
⇒ x' ± Z( σ/√n )
⇒ 34.2 ± 1.96( 40/√33 )
⇒ 34.2 ± 13.647
so
we have
( 34.2 - 13.647 ), ( 34.2 + 13.647 )
⇒ ( 20.6, 47.8 )
Therefore, 95% confidence interval for the mean duration of imprisonment μ of all political prisoners with PTSD is between 20.6 months and 47.8 months.