To solve this problem, let us proceed step by step:

a. Subjective Examination of the Scatterplot

Look at the overall pattern of the 10 points in the scatterplot:

• If the points follow a straight-line pattern closely, there is a strong correlation.
• If the points are widely scattered or show no clear direction, there is weak or no correlation.

Based on your observation:

• Is there a linear pattern?
• Are there any outliers (like the point (9, 2)) that deviate significantly from the overall trend?

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b. Calculate the Correlation Coefficient (r)

The formula for the correlation coefficient $r$ is: [ r = \frac{n \sum (x y) - \sum x \sum y}{\sqrt{[n \sum x^2 - (\sum x)^2][n \sum y^2 - (\sum y)^2]}} ] Where:

• $n$ = number of points
• $\sum x$, $\sum y$ = sums of the $x$ and $y$ values
• $\sum (xy)$, $\sum x^2$, $\sum y^2$ = sums of products, squares of $x$, and squares of $y$

Once $r$ is calculated:

• Compare $|r|$ with the critical value from the table of critical values for the correlation coefficient to determine if the correlation is significant.

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c. Remove the Point (9, 2)

Recalculate $r$ without the point (9, 2) using the same formula as above.

• Observe whether removing the point changes the correlation coefficient significantly.
• Compare $|r|$ with the critical value again to assess the impact on significance.

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d. Conclusion

Discuss the impact of removing the point (9, 2):

• Does this single pair of values (9, 2) influence the correlation coefficient substantially?
• What does this imply about the sensitivity of correlation to outliers?

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Would you like me to calculate these values for you if you provide the dataset or if I analyze based on an uploaded image?