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.

Question

Quizplus · Accepted Answer

EStatement C is not necessarily true because in a paired t-test, the observations within each pair are related or matched, not independent. The independence assumption in a paired t-test applies to the pairs themselves, not the observations within each pair. Statement E is incorrect because it contradicts the identification of a false statement, given that C is not necessarily true.

Which of the Following Statements Are Not Necessarily True About (X1,Y1),(X2,Y2),……,(Xn,Yn)\left( X _ { 1 } , Y _ { 1 } \right) , \left( X _ { 2 } , Y _ { 2 } \right) , \ldots \ldots , \left( X _ { n } , Y _ { n } \right)(X1​,Y1​),(X2​,Y2​),……,(Xn​,Yn​)

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