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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Description: 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

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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

mu 1 equals

The mean brain volume of all obsessive-compulsive people

mu 2 equals

The mean brain volume of all healthy persons

mu 1 equals

The mean test score of all obsessive-compulsive people

mu 2 equals

The mean test score of all healthy persons

mu 1 equals

The mean brain volume of 10 obsessive-compulsive patients

mu 2 equals

The mean brain volume of 10 healthy persons

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

Upper H 0 : mu 1 equals mu 2 Upper H 1 : mu 1 greater than mu 2

Upper H 0 : mu 1 equals

1390.03

Upper H 1 : mu 2 equals

1275.94

Upper H 0 : mu 1 equals mu 2 Upper H 1 : mu 1 less than mu 2

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?

0.1029

0.1151

0.0917

0.1015

d. State the technical conclusion

Do not reject Upper H 0

Reject Upper H 0

e. State the final conclusion

There is not sufficient evidence to warrant rejection of the claim.

There is sufficient evidence to warrant rejection of the claim.

There is not sufficient sample evidence to support the claim.

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?

Yes

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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