Which of the Following Statements Are True When $\bar { X }$

question 17

Multiple Choice

Which of the following statements are true when $\bar { X }$ is the mean of a random sample of size n from a normal distribution with mean $\mu$ ?

• A) The random variable \(Z = ( \bar { X } - \mu ) / ( S / \sqrt { n ) }\)
• Has approximately a standard normal distribution for large n.
• B) The random variable \(T = ( \bar { X } - \mu ) / ( S / \sqrt { n ) }\)
• Has a t-distribution with n-1 degrees of freedom for small n.
• C) The normal distribution is governed by two parameters, the mean \(\mu\)
• And the standard deviation \(\sigma\)
• )
• D) A t-distribution is governed by only one parameter, called the number of degrees of freedom.
• E) All of the above answers are true.

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Definitions:

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A blood test that measures how quickly red blood cells settle at the bottom of a test tube, indicating the presence of inflammation in the body.

Fibrin

A fibrous, non-globular protein involved in the clotting of blood, formed by the action of the enzyme thrombin on fibrinogen.

Leukapheresis

A medical procedure that involves the separation and removal of white blood cells from the blood.

Erythrocyte Sedimentation Rate (ESR)

A blood test that measures how quickly erythrocytes (red blood cells) settle at the bottom of a test tube that contains a blood sample.