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

Explanation:

Step1: Recall correlation - coefficient formula

The formula for the correlation coefficient $r$ is $r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}}$. Let $x$ be the time spent at the dentist and $y$ be the 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

$n\sum y^{2}-(\sum y)^{2}=4\times877475-1473^{2}=3509900 - 2169729=1340171$. The product of the two parts of the denominator is $\sqrt{7.8875\times1340171}=\sqrt{10571708.625}\approx3251.416$.

Step5: Calculate the correlation coefficient

$r=\frac{3022.75}{3251.416}\approx0.93$.

Answer:

0.93