Question

Preliminary analyses indicate that you can consider the assumptions for using nonpooled​ t-procedures satisfied. Researchers randomly and independently selected 29 prisoners diagnosed with chronic posttraumatic stress disorder​ (PTSD) and 21 prisoners that were diagnosed with PTSD but had since recovered​ (remitted).

Chronic Remitted
x1 ​= 29.7 x2 ​= 22.6
s1 ​= 3 s2 ​= 9
n1 ​= 29 n2 ​= 21

Obtain a 95​% confidence interval for the​ difference, µ1 - µ2​, between the mean ages at arrest for prisoners with chronic PTSD and remitted PTSD.

Answer 1

(2.880, 11.320)

Explanation:

Keep in mind the formula for a 2-sample t-interval.

t = x1 - x2 ± t*
`\sqrt{(s1^(2))/(n1) +(s2^(2))/(n2) }`

First calculate df the degrees of freedom and t* the critical t.

df = 23.24 (from technology: STAT->TEST->0)

t* = invt(.975, 23.24) = 2.067

Now plug them in and solve.

t = x1 - x2 ± t*
`\sqrt{(s1^(2))/(n1) +(s2^(2))/(n2) }`

= 29.7 - 22.6 ± 2.067
`\sqrt{(3^(2))/(29) +(9^(2))/(21) }`

= 7.1 ± 4.220

= (2.880, 11.320)