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

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.