Which of the Following Statements Are Not Necessarily True About $\left( X _ { 1 } , Y _ { 1 } \right) , \left( X _ { 2 } , Y _ { 2 } \right) , \ldots \ldots , \left( X _ { n } , Y _ { n } \right)$

question 25

Multiple Choice

Which of the following statements are not necessarily true about the paired t test?

• A) The data consists of n independently selected pairs \(\left( X _ { 1 } , Y _ { 1 } \right) , \left( X _ { 2 } , Y _ { 2 } \right) , \ldots \ldots , \left( X _ { n } , Y _ { n } \right)\)
• B) The differences \(X _ { 1 } - Y _ { 1 } , X _ { 2 } - Y _ { 2 } , \ldots \ldots , X _ { n } - Y _ { n }\)
• Are assumed to be normally distributed.
• C) The X and Y observations within each pair \(\left( X _ { 1 } , Y _ { 1 } \right) , \left( X _ { 2 } , Y _ { 2 } \right) , \ldots \ldots , \left( X _ { n } , Y _ { n } \right)\)
• Are independent.
• D) The \(\bar { X } \text { and } \bar { Y }\)
• Are not independent of one another.
• E) All of the above statements are true.

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Definitions:

Mental Processes

Internal cognitive operations that enable consciousness, perception, thinking, judgement, and memory, allowing humans to interpret and interact with the world around them.

Cognitive Perspective

A psychological approach that focuses on the mental processes involved in knowing, including thinking, memory, problem-solving, and language.

Gestalt Psychologists

Psychologists who study how people integrate and perceive sensory information into meaningful wholes, emphasizing the importance of context and the whole pattern over the sum of its parts.

Humanistic Psychology

The school of psychology that focuses on the uniqueness of human beings and their capacity for choice, growth, and psychological health.