Question

the table shows the number of hours students spend reading, x, and the number of pages read, y, over the course of a week. what does the correlation coefficient for the data indicate about the linear association between the number of hours students spend reading books per week and the number of pages read? there is a strong negative linear association. there is a strong positive linear association. there is a weak negative linear association. there is a weak positive linear association

Explanation:

Step1: Analyze the trend of data

As the number of hours spent reading (\(x\)) increases (from \(1\) to \(3\) to \(5\) etc.), the number of pages read (\(y\)) also increases (from \(20\) to \(55\) to \(90\) etc.). This indicates a positive association.

Step2: Check the strength of the association

Calculate the differences:

• When \(x\) increases by \(2\) (from \(1\) to \(3\)), \(y\) increases by \(35\) (\(55 - 20\)).
• When \(x\) increases by \(2\) (from \(3\) to \(5\)), \(y\) increases by \(35\) (\(90 - 55\)).
• When \(x\) increases by \(2\) (from \(5\) to \(7\)), \(y\) increases by \(30\) (\(120 - 90\)).
• When \(x\) increases by \(2\) (from \(7\) to \(9\)), \(y\) increases by \(40\) (\(160 - 120\)).
• When \(x\) increases by \(2\) (from \(9\) to \(11\)), \(y\) increases by \(20\) (\(180 - 160\)).

The change in \(y\) for a constant change in \(x\) is relatively consistent. So, it is a strong association.

Answer:

There is a strong positive linear association.