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:

Conscientiousness

A personality trait characterized by diligence, carefulness, and the desire to do a task well, often associated with high levels of responsibility.

Big Five Personality Traits

are five broad dimensions of personality used to describe human character traits: openness, conscientiousness, extraversion, agreeableness, and neuroticism.

Responsible, Dependable, Careful

describes attributes of an individual who is reliable, can be trusted to complete tasks, and takes precautions to avoid mistakes.

Projection

The act of estimating or predicting future trends based on current or historical data.