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). Values of $r$ range from - 1 to 1, where $|r| = 1$ is a perfect linear relationship and $r = 0$ means no linear relationship.

Step2: Analyze the data trend

As the time spent at the dentist increases (from 0.75 hours to 2.7 hours), the bill amount also generally increases (from $156 to $867). So, we expect a positive correlation coefficient.

Step3: Eliminate negative - correlation options

Options - 0.93 and - 0.27 can be eliminated since they represent negative correlations.

Step4: Consider the strength of the relationship

The data points seem to follow a relatively strong linear pattern. A correlation coefficient of 0.27 would indicate a weak positive correlation, while a value of 0.93 indicates a strong positive correlation. Given the general upward - trend of the data, the correlation coefficient is likely to be 0.93.

Answer:

0.93