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

Explanation:

Step1: Recall correlation coefficient formula

The formula for the sample - correlation coefficient $r$ is $r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}}$, where $n$ is the number of data points, $x$ is the independent variable (time spent at the dentist), and $y$ is the dependent variable (bill amount). Let $x =$ time spent at the dentist and $y=$ bill amount. We have $n = 4$. $\sum x=1.4 + 2.7+0.75 + 1.6=6.45$ $\sum y=235 + 867+156 + 215 = 1473$ $\sum xy=(1.4\times235)+(2.7\times867)+(0.75\times156)+(1.6\times215)$ $=329+2340.9 + 117+344=3130.9$ $\sum x^{2}=1.4^{2}+2.7^{2}+0.75^{2}+1.6^{2}=1.96 + 7.29+0.5625 + 2.56=12.3725$ $\sum y^{2}=235^{2}+867^{2}+156^{2}+215^{2}=55225+751689+24336+46225=877475$

Step2: Calculate the numerator

$n(\sum xy)-(\sum x)(\sum y)=4\times3130.9-6.45\times1473$ $=12523.6-9500.85 = 3022.75$

Step3: Calculate the first part of the denominator

$n\sum x^{2}-(\sum x)^{2}=4\times12.3725-(6.45)^{2}$ $=49.49 - 41.6025=7.8875$

Step4: Calculate the second part of the denominator

$n\sum y^{2}-(\sum y)^{2}=4\times877475-(1473)^{2}$ $=3509900 - 2169729=1340171$

Step5: Calculate the denominator

$\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}=\sqrt{7.8875\times1340171}\approx\sqrt{10564490.525}\approx3249.08$

Step6: Calculate the correlation coefficient

$r=\frac{3022.75}{3249.08}\approx0.93$

Answer:

$0.93$