Question

According to a study of political​ prisoners, the mean duration of imprisonment for

30 prisoners with chronic​ post-traumatic stress disorder​ (PTSD) was 31.3 months. Assuming that sigmaσequals=41

​months, determine a 90​% confidence interval for the mean duration of​ imprisonment, muμ​,

of all political prisoners with chronic PTSD. Interpret your answer in words

A 90% confidence level for the population means is from months to months

Answer 1

population std dev ,    σ =    41.0000
Sample Size ,   n =    30
Sample Mean,    x̅ =   31.3000

Level of Significance ,    α =    0.10   
'   '   '          
z value=   z α/2=   1.6449 [Excel formula =NORMSINV(α/2) ]      
                  
Standard Error , SE = σ/√n =   41.000   / √   30   =   7.4855
margin of error, E=Z*SE =   1.6449   *   7.486   =   12.313
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    31.30   -   12.313   =   18.9874
Interval Upper Limit = x̅ + E =    31.30   -   12.313   =   43.6126

A 90% confidence level for the population means is from 18.99 months to 43.61 months

===========================

we are 90% confident that true population mean duration of​ imprisonment, μ​,of all political prisoners with chronic PTSD lies within confidence interval