According to a study of political prisoners, the mean duration of imprisonment for 30 prisoners with chronic post-traumatic stress disorder (PTSD) was 30.6 months. Assuming that sigmaequals42 months, determine a 95% confidence interval for the mean duration of imprisonment, mu, of all political prisoners with chronic PTSD. Interpret your answer in words.

The 95% confidence interval for the mean duration of imprisonment, mu, of all political prisoners with chronic PTSD is between 15.57 months and 45.63 months.

This means that we are 95% sure that the true mean mean duration of imprisonment, mu, of all political prisoners with chronic PTSD is between 15.57 months and 45.63 months.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 30.6 - 15.03 = 15.57 months

The upper end of the interval is the sample mean added to M. So it is 30.6 + 15.03 = 45.63 months

The 95% confidence interval for the mean duration of imprisonment, mu, of all political prisoners with chronic PTSD is between 15.57 months and 45.63 months.

This means that we are 95% sure that the true mean mean duration of imprisonment, mu, of all political prisoners with chronic PTSD is between 15.57 months and 45.63 months.

answer: 4

step-by-step explanation: