Question

According to a study of political​ prisoners, the mean duration of imprisonment for 32 prisoners with chronic​ post-traumatic stress disorder​ (PTSD) was 31.8 months. Assuming that sigma equals 35 ​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.

A 95% confidence interval for the population mean is from _____months to ______ months?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 31.8

Population standard deviation =    = 35

Sample size = n =32

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z/2 * ( /n)

= 1.96* ( 35 /  32 )

= 12.1269
At 95% confidence interval estimate of the population mean
is,

- E < < + E

31.8 - 12.1269 <   < 31.8+12.1269

19.6731 <   < 43.9269

( 19.6731 , 43.9269 )