Question

the police department tracked the number of ticket writers and number of tickets issued for the past 8 weeks. the scatter plot shows the results. which statement is true? more ticket writers results in more tickets issued. more ticket writers results in fewer tickets issued. there were 50 tickets issued every week. when there are 10 ticket writers, there will be 800 tickets issued.

Explanation:

Step1: Analyze the scatter - plot trend

In a scatter - plot, if the points generally move from the lower left to the upper right, there is a positive correlation. If they move from the upper left to the lower right, there is a negative correlation.
Looking at the scatter - plot of the number of ticket writers (x - axis) and the number of tickets issued (y - axis), as the number of ticket writers (x) increases, the number of tickets issued (y) also increases. This indicates a positive correlation.

Step2: Evaluate each option

• Option 1 (Yellow box):

Since there is a positive correlation (as x (number of ticket writers) increases, y (number of tickets issued) increases), the statement “More ticket writers results in more tickets issued” is consistent with the positive - correlation trend of the scatter - plot.

• Option 2 (Purple box):

A negative correlation (more ticket writers resulting in fewer tickets issued) would mean the points move from upper left to lower right. But our scatter - plot has a positive trend, so this option is wrong.

• Option 3 (Orange box):

If there were 50 tickets issued every week, the scatter - plot would have all the points on the horizontal line \(y = 50\). But the y - values (number of tickets) vary, so this option is wrong.

• Option 4 (Green box):

We cannot assume a specific linear relationship (to say when \(x = 10\), \(y=800\)) just from the scatter - plot. There is no indication of a linear equation \(y=mx + b\) that would give this exact value for \(x = 10\) from the general positive - correlation scatter - plot.

Answer:

More ticket writers results in more tickets issued.