A study used​ x-ray computed tomography​ (CT) to collect data on brain volumes for a group of patients with​ obsessive-compulsive disorders and a control group of healthy persons. Sample results​ (in mL) are given below for total brain volumes. Use a 0.05 significance level to test the claim that there is no difference between the mean for​ obsessive-compulsive patients and the mean for healthy persons.   ​Obsessive-compulsive patients: n​ = 10, x overbar equals 1390.03 ​, s​ = 156.84                          Control​ group: n​ = 10, x overbar equals 1275.94 ​, s​ = 137.97 a. Define the parameters     A. mu 1 equals   The mean brain volume of all​ obsessive-compulsive people mu 2 equals   The mean brain volume of all healthy persons   B. mu 1 equals   The mean test score of all​ obsessive-compulsive people mu 2 equals   The mean test score of all healthy persons   C. mu 1 equals   The mean brain volume of 10​ obsessive-compulsive patients mu 2 equals   The mean brain volume of 10 healthy persons   D. p 1 equals   The proportion of all people with​ obsessive-compulsive disorders p 2 equals   The proportion of all people who are healthy   b. State the null and alternative hypotheses     A. Upper H 0 : mu 1 equals mu 2 Upper H 1 : mu 1 greater than mu 2     B. Upper H 0 : mu 1 equals 1390.03    Upper H 1 : mu 2 equals 1275.94     C. Upper H 0 : mu 1 equals mu 2 Upper H 1 : mu 1 less than mu 2     D. Upper H 0 : mu 1 equals mu 2 Upper H 1 : mu 1 not equals mu 2     c. Calculate the​ P-value. Which of these options is closest to its​ value?     A. 0.1029

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A study used​ x-ray computed tomography​ (CT) to collect data on brain volumes for a group of patients with​ obsessive-compulsive disorders and a control group of healthy persons. Sample results​ (in mL) are given below for total brain volumes. Use a 0.05 significance level to test the claim that there is no difference between the mean for​ obsessive-compulsive patients and the mean for healthy persons.
 
​Obsessive-compulsive patients: n​ = 10,
x overbar equals

1390.03

​,
s​ = 156.84
                         Control​ group: n​ = 10,
x overbar equals

1275.94

​,
s​ = 137.97
a. Define the parameters
 
 
A.
mu 1 equals
 
The mean brain volume of all​ obsessive-compulsive people
mu 2 equals
 
The mean brain volume of all healthy persons
 
B.
mu 1 equals
 
The mean test score of all​ obsessive-compulsive people
mu 2 equals
 
The mean test score of all healthy persons
 
C.
mu 1 equals
 
The mean brain volume of 10​ obsessive-compulsive patients
mu 2 equals
 
The mean brain volume of 10 healthy persons
 
D.
p 1 equals
 
The proportion of all people with​ obsessive-compulsive disorders
p 2 equals
 
The proportion of all people who are healthy
 
b. State the null and alternative hypotheses
 
 
A.
Upper H 0 : mu 1 equals mu 2 Upper H 1 : mu 1 greater than mu 2
 
 
B.
Upper H 0 : mu 1 equals

1390.03

  
Upper H 1 : mu 2 equals

1275.94

 
 
C.
Upper H 0 : mu 1 equals mu 2 Upper H 1 : mu 1 less than mu 2
 
 
D.
Upper H 0 : mu 1 equals mu 2 Upper H 1 : mu 1 not equals mu 2
 
 
c. Calculate the​ P-value. Which of these options is closest to its​ value?
 
 
A.
0.1029
 
 
B.
0.1151
 
 
C.
0.0917
 
 
D.
0.1015
 
 
d. State the technical conclusion
 
 
A.
Do not reject Upper H 0
 
 
B.
Reject Upper H 0
 
 
e. State the final conclusion
 
 
A.
There is not sufficient evidence to warrant rejection of the claim.
 
B.
There is sufficient evidence to warrant rejection of the claim.
 
C.
There is not sufficient sample evidence to support the claim.
 
D.
The sample data support the claim.
 
f. Does it appear that the total brain volume can be used as an indicator of​ obsessive-compulsive disorders?
 
 
A.
No
 
B.
Yes
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