Preliminary data analyses indicate that you can consider the assumptions for using nonpooled​ t-procedures satisfied. Researchers randomly and independently selected 30 prisoners diagnosed with chronic posttraumatic stress disorder​ (PTSD) and 22 prisoners that were diagnosed with PTSD but had since recovered​ (remitted). The​ ages, in​ years, at arrest yielded the summary statistics shown in the table to the right. At the 10​% significance​ level, do the data provide sufficient evidence to conclude that a difference exists in the mean age at arrest of prisoners with chronic PTSD and remitted​ PTSD? Chronic Remitted x1 = 28.2 x2 = 20.9 s1 = 5 s2 = 6 n1 = 30 n2 = 22   What are the hypotheses for the nonpooled​ t-test?   A. H0​: μ1≥μ2 Ha​: μ1<μ2   B. H0​: μ1=μ2 Ha​: μ1<μ2   C. H0​: μ1=μ2 Ha​: μ1>μ2   D. H0​: μ1=μ2 Ha​: μ1≠μ2   Find the test statistic.   t=___________ ​(Round to three decimal places as​ needed.)   Find the critical​ value(s).   __________________ ​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)   What is the conclusion of the hypothesis​ test?     _______________ (Reject or Do not reject) the null​ hypothesis, meaning that the data ____________ (do not provide or provide) sufficient evidence to conclude that a difference exists in the mean age at arrest of prisoners with chronic PTSD and remitted PTSD.

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Preliminary data analyses indicate that you can consider the assumptions for using nonpooled​ t-procedures satisfied. Researchers randomly and independently selected 30 prisoners diagnosed with chronic posttraumatic stress disorder​ (PTSD) and 22 prisoners that were diagnosed with PTSD but had since recovered​ (remitted). The​ ages, in​ years, at arrest yielded the summary statistics shown in the table to the right. At the 10​% significance​ level, do the data provide sufficient evidence to conclude that a difference exists in the mean age at arrest of prisoners with chronic PTSD and remitted​ PTSD?

Chronic
Remitted
x1
=
28.2
x2
=
20.9
s1
=
5
s2
=
6
n1
=
30
n2
=
22

 

What are the hypotheses for the nonpooled​ t-test?
 
A. H0​: μ1≥μ2 Ha​: μ1<μ2
 
B. H0​: μ1=μ2 Ha​: μ1<μ2
 
C. H0​: μ1=μ2 Ha​: μ1>μ2
 
D. H0​: μ1=μ2 Ha​: μ1≠μ2
 
Find the test statistic.
 
t=___________
​(Round to three decimal places as​ needed.)
 
Find the critical​ value(s).
 
__________________
​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)
 
What is the conclusion of the hypothesis​ test?
 
 
_______________ (Reject or Do not reject) the null​ hypothesis, meaning that the data ____________ (do not provide or provide) sufficient evidence to conclude that a difference exists in the mean age at arrest of prisoners with chronic PTSD and remitted PTSD.
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