Answer :
To determine which value for \(Y\) would be least likely to indicate an association between the variables in the given table, we need to look at the proportions for each option and relate them to the marginal totals.
Given the table:
[tex]\[ \begin{tabular}{|c|c|c|c|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & [tex]$A$[/tex] & [tex]$B$[/tex] & Total \\
\hline[tex]$C$[/tex] & [tex]$X$[/tex] & 0.25 & [tex]$G$[/tex] \\
\hline[tex]$D$[/tex] & [tex]$Y$[/tex] & 0.68 & [tex]$H$[/tex] \\
\hline[tex]$E$[/tex] & [tex]$Z$[/tex] & 0.07 & [tex]$J$[/tex] \\
\hline Total & 1.0 & 1.0 & 1.0 \\
\hline
\end{tabular}
\][/tex]
The total for column \(B\) is 1.0, meaning all values in column \(B\) sum up to 1.0.
We have the options for \(Y\) as:
- 0.06
- 0.24
- 0.69
- 1.0
To find the value of \(Y\) that indicates the least likely association between the variables, we need to find the value that is closest to the marginal proportion for column \(B\), which in this case is the total for column \(B\), 1.0.
By comparing each option:
- 0.06 is quite far from 1.0.
- 0.24 is also relatively far from 1.0.
- 0.69 is closer to 1.0, but still not the same.
- 1.0 is exactly equal to the total for column \(B\).
Hence, the value of [tex]\(Y\)[/tex] that is least likely to indicate an association between the variables is [tex]\(\boxed{1.0}\)[/tex].
Given the table:
[tex]\[ \begin{tabular}{|c|c|c|c|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & [tex]$A$[/tex] & [tex]$B$[/tex] & Total \\
\hline[tex]$C$[/tex] & [tex]$X$[/tex] & 0.25 & [tex]$G$[/tex] \\
\hline[tex]$D$[/tex] & [tex]$Y$[/tex] & 0.68 & [tex]$H$[/tex] \\
\hline[tex]$E$[/tex] & [tex]$Z$[/tex] & 0.07 & [tex]$J$[/tex] \\
\hline Total & 1.0 & 1.0 & 1.0 \\
\hline
\end{tabular}
\][/tex]
The total for column \(B\) is 1.0, meaning all values in column \(B\) sum up to 1.0.
We have the options for \(Y\) as:
- 0.06
- 0.24
- 0.69
- 1.0
To find the value of \(Y\) that indicates the least likely association between the variables, we need to find the value that is closest to the marginal proportion for column \(B\), which in this case is the total for column \(B\), 1.0.
By comparing each option:
- 0.06 is quite far from 1.0.
- 0.24 is also relatively far from 1.0.
- 0.69 is closer to 1.0, but still not the same.
- 1.0 is exactly equal to the total for column \(B\).
Hence, the value of [tex]\(Y\)[/tex] that is least likely to indicate an association between the variables is [tex]\(\boxed{1.0}\)[/tex].
