reliminary data anayses indicate that you can consider the assumpsons for using
ID: 3231829 • Letter: R
Question
reliminary data anayses indicate that you can consider the assumpsons for using nonpooled t procedures satisfied Researchers randomly and independently selected 34 risoners diagnosed with chronic posttraumatic stress disorder (PTsD) and21 prisoners that were diagnosed with PTsD but had recovered (remited). The ages in at 251 233 mest yielded the summary statistics shown in the table to the right Al the 10% signscanoe level, do the data provide suffcient evidence to conclude that a di in the mean age at arrest prisoners with chronicPTSD remitted PTsD? 1.2 sh 7 what are the hypotheses for the nonpooled test? Find he test statistic. (Round to free decima piaces as reeded Find the Pvalue (Round four deomal heeded What is te condusion ofthe hypothesis tost? sunoortevidence tocondudethat a dnerenca exists inthe mean age at of prisoners with chronic PTSD and remitted PTSD Click to select your answers), minitab 17.3Explanation / Answer
(a) Option D
(b)
Data:
n1 = 34
n2 = 21
x1-bar = 25.1
x2-bar = 23.3
s1 = 2
s2 = 7
Hypotheses:
Ho: 1 = 2
Ha: 1 2
Decision Rule:
= 0.1
Degrees of freedom = 34 + 21 - 2 = 53
Lower Critical t- score = -1.674116237
Upper Critical t- score = 1.674116237
Reject Ho if |t| > 1.674116237
Test Statistic:
Pooled SD, s = [{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] = (((34 - 1) * 2^2 + (21 - 1) * 7^2)/(34 + 21 -2)) = 4.581
SE = s * {(1 /n1) + (1 /n2)} = 4.58051657299389 * ((1/34) + (1/21)) = 1.27129605
t = (x1-bar -x2-bar)/SE = 1.416
(c) p- value = 0.1627
(d) Decision (in terms of the hypotheses):
Since 1.415877914 < 1.674116237 we fail to reject Ho
Conclusion (in terms of the problem):
There is no evidence of a difference between the means
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