Let's start by analyzing the tasks presented in the image:

(a) Display the data in a scatter plot:

From the available options, the scatter plot labeled C is selected as correct. It shows vocabulary size on the y-axis and age in years on the x-axis, which seems to match the description of the relationship between these variables.

(b) Calculate the sample correlation coefficient $r$:

To calculate $r$, we need the actual data (ages and vocabulary sizes). While the image shows instructions, the data itself isn't visible. The Pearson correlation coefficient $r$ is calculated using the formula:

[ r = \frac{n(\Sigma xy) - (\Sigma x)(\Sigma y)}{\sqrt{[n \Sigma x^2 - (\Sigma x)^2][n \Sigma y^2 - (\Sigma y)^2]}} ]

Where:

• $n$ = number of data points
• $x$ = age values
• $y$ = vocabulary size values

If you can provide the data table (either typing it or uploading it as an image), I can proceed to compute the sample correlation coefficient for you.

Would you like to share the data or ask for more details?

Here are 5 questions to expand on the current topic:

1. How is Pearson’s correlation coefficient used to measure the strength of a linear relationship?
2. What are the conditions to use the Pearson correlation coefficient?
3. How can scatter plots help in identifying the nature of the correlation?
4. What is the difference between positive, negative, and zero correlation?
5. How do outliers in the data affect the correlation coefficient?

Tip: Always check the assumptions (linearity, no outliers, etc.) before interpreting a Pearson correlation coefficient.