Consider the Data Set Shown $\begin{array}{|rr|}\hline \underline{x} & \underline{y} \\7 & 5 \\7 & 8 \\9 & 7 \\11 & 9 \\12 & 8 \\16 & 11\\\hline\end{array}$

question 18

Essay

Consider the data set shown. Conduct a full correlation analysis on these values.
​
$\begin{array}{|rr|}\hline \underline{x} & \underline{y} \\7 & 5 \\7 & 8 \\9 & 7 \\11 & 9 \\12 & 8 \\16 & 11\\\hline\end{array}$ (a) Make a graph of the data points.
(b) Calculate the correlation coefficient with 95% confidence interval.
(c) Calculate the t-value for the correlation coefficient.
(d) Using your results from (b) and (c), make a statement about the significance of the association between the X and Y values.

---

Definitions:

Majority Determining

The process by which the greater number or majority's choice decides an outcome in a decision-making context.

Condorcet Paradox

A situation in social choice theory where collective preferences can be cyclical, even if the preferences of individual members are not, leading to a lack of transitivity in voting outcomes.

Transitive Preferences

A consistency in choice such that if an individual prefers option A to B and B to C, then they will also prefer A to C.

Arrow's Impossibility Theorem

A principle in social choice theory stating that no rank-order voting system can be designed that always satisfies a set of fair criteria when there are three or more options.