19. A teacher records the amount of time it took a random sample of students to finish a test and their scores on that test. Let $x$ be the score and $y$ be the amount of time. Conduct a hypothesis test of the claim that there is a linear correlation between the variables, using a 0.10 level of significance.
$\begin{array}{cc}\text { score (percent) } & \text { time (min.) } \\ 80 & 45 \\ 75 & 48 \\ 70 & 40 \\ 90 & 50 \\ 95 & 40 \\ 100 & 30 \\ 75 & 30 \\ 60 & 49 \\ 75 & 38 \\ 95 & 55\end{array}$
Find the BEST PREDICTED VALUE of $y$ for $x=60$.

Step 1 ：Given the scores (x) and the time (y) as follows: x = [ 80, 75, 70, 90, 95, 100, 75, 60, 75, 95] and y = [45, 48, 40, 50, 40, 30, 30, 49, 38, 55].

Step 2 ：We are asked to find the best predicted value of y for x=60. This requires us to perform a linear regression on the given data.

Step 3 ：Linear regression is a statistical method that allows us to study the relationship between two continuous quantitative variables. In this case, we are interested in the relationship between the score (x) and the time (y).

Step 4 ：The general form of a linear regression equation is \(y = mx + b\), where m is the slope of the line and b is the y-intercept.

Step 5 ：First, we need to calculate the slope (m) and the y-intercept (b) of the regression line. Then, we can substitute x=60 into the equation to find the predicted value of y.

Step 6 ：After performing the calculations, we find that the predicted value of y for x=60 is approximately 43.53743760399335.

Step 7 ：Rounding to two decimal places, the best predicted value of y for x=60 is \(\boxed{43.54}\).