For part (a), the correct scatter plot is option A. This plot shows a positive relationship between age (in years) and vocabulary size, which is consistent with typical growth patterns in vocabulary as children age.

For part (b), to calculate the sample correlation coefficient $r$, you would need the actual numerical data points for the ages and vocabulary sizes of the children. If the data points are accessible, I can help you calculate $r$ using the formula:

$r = \frac{\sum \left( x - \bar{x} \right)\left( y - \bar{y} \right)}{\sqrt{\sum \left( x - \bar{x} \right)^2 \sum \left( y - \bar{y} \right)^2}}$

where $x$ and $y$ are the age and vocabulary size values, respectively, and $\bar{x}$ and $\bar{y}$ are their means.

Do you have the data values to proceed with this calculation?

Follow-up Questions:

1. Do you have the actual data points to calculate the correlation coefficient?
2. Would you like an explanation of the formula for the correlation coefficient?
3. Do you need help interpreting what a positive or negative $r$ value indicates?
4. Would you like guidance on how to input data into a calculator or software to find $r$?
5. Are there any additional parts to this question that need addressing?

Tip: Correlation coefficients range from -1 to +1, where values close to +1 indicate a strong positive relationship and values close to -1 indicate a strong negative relationship.