Question

# A 95 % confidence interval of 16.2 months to 50.2 months has been found for the...

A 95 % confidence interval of 16.2 months to 50.2 months has been found for the mean duration of imprisonment, mu , of political prisoners of a certain country with chronic PTSD.

a. Determine the margin of error, E.

b. Explain the meaning of E in this context in terms of the accuracy of the estimate.

c. Find the sample size required to have a margin of error of 11 months and a 99 % confidence level. (Use sigma equals 45 months.)

d. Find a 99 % confidence interval for the mean duration of imprisonment, mu , if a sample of the size determined in part (c) has a mean of 36.1 months.

a. Since the confidence interval is 16.2 to 50.2 then the mean will be (16.2+50.2)/2=33.2 and hence margin of error would be 33.2-16.2=17 or 50.3-33.2=17

b. The machine of error that is calculated here as 17 means that we can be 95% confident that the mean of the population lies within +/- 17 month of the sample mean.

c. The minimum sample size is calculated as

Z value is calculated from excel tool or by Z table shown below as 2.58 .

d. Since the margin of error is 11 in the part c and sample size is 112 at 99% confidence level hence

Confidence interval will be

Mean+/E

=36.1+/-11

={25.1, 47.1}