Question

A 95 % confidence interval of 16.5 months to
50.5 months has been found for the mean duration of imprisonment, ?, 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 13 months and a 99 %confidence level. (Use ? =45 months.)

d. Find a 99 % confidence interval for the mean duration of imprisonment, ? , if a sample of the size determined in part (c) has a mean of 36.4 months.

Answer 1

A 95 % confidence interval of 16.5 months to 50.5 months has been found for the mean duration of imprisonmen ? of political prisoners of a certain country with chronic PTSD.

A)Determine the margin of error, E.

Now to determine the margin of error,

= (50.5-16.5)/2

= 17

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

This is the margin of error from the mean, given 95% confidence, for this particular sample.

Based on the definition of a confidence interval: one can be 95% confident that the interval 15.9 mths to 50.5 mths contains the mean duration of imprisonment,population mean, of the prisoners.

c. Find the sample size required to have a margin of error of 13 months and a 99 %confidence level.

(Use ?= =45 months.)

N= (z*sd/e)^2

= (2.5758*45/13)^2

=79.499

This gets rounded up to:

n= 80

d. Find a 99 % confidence interval for the mean duration of imprisonment, ? if a sample of the size determined in part (c) has a mean of 36.4 months.

The margin of error, from that part, was set to be 13 months, so the interval is:

= 36.4 ± 13

= (23.4 to 49.4)