Question

the table shows the time a patient spends at the dentist and the amount of the bill. bill amount for time spent at the dentist

time spent at the dentist (in hours)	bill amount
2.7	$867
0.75	$156
1.6	$215

what is the correlation coefficient for the data in the table?

• -0.93
• -0.27
• 0.27
• 0.93

Explanation:

Step1: Recall correlation coefficient concept

The correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables. A positive \(r\) indicates a positive linear - relationship (as one variable increases, the other increases), and a negative \(r\) indicates a negative linear - relationship (as one variable increases, the other decreases). The closer \(|r|\) is to 1, the stronger the linear relationship.

Step2: Analyze the data trend

As the time spent at the dentist (in hours) increases, the bill amount also generally increases. For example, when the time changes from \(0.75\) hours (\(\$156\)) to \(1.4\) hours (\(\$235\)), and from \(1.4\) hours to \(2.7\) hours (\(\$867\)), the bill amount goes up. So, we expect a positive correlation coefficient.

Step3: Eliminate negative - correlation options

We can eliminate the options \(- 0.93\) and \(-0.27\) since we have a positive - trending relationship.

Step4: Consider the strength of the relationship

The relationship seems to be relatively strong as the increase in time is accompanied by a noticeable increase in the bill amount. A correlation coefficient of \(0.27\) indicates a weak positive relationship, while \(0.93\) indicates a strong positive relationship. So, the correlation coefficient is \(0.93\).

Answer:

D. \(0.93\)