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in Math CRN 10106
miranda starling
$11 / 21 / 23$ 4:25 PM
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Question 8, 12.6.44
HW Score: $27.27 \%, 30$ of 110
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A gallon of chlorine is put into a swimming pool. Each hour later for the following 6 hours the percent of chlorine that remains in the pool is measured. The following information is obtained. Use the data provided in the table to complete parts a) through d).
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline Time & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline \begin{tabular}{c}
Chlorine \\
remaining (percent)
\end{tabular} & 84.7 & 70.7 & 65.6 & 47.2 & 32.2 & 20.5 \\
\hline
\end{tabular}
(i) Click the icon to view the correlation coefficient, $r$, for various values of $n$ and $\alpha$.
a) Determine the correlation coefficient for time and percent of chlorine remaining.
The correlation coefficient between time and percent of chlorine remaining is $r=\square$.
(Type an integer or decimal rounded to the nearest thousandth as needed.)
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Answer
Rounding to the nearest thousandth, we get the final answer: The correlation coefficient between time and percent of chlorine remaining is \( r = \boxed{-0.993} \).
Step 1 ：Given the data of time and percent of chlorine remaining, we are asked to find the correlation coefficient between these two variables.
Step 2 ：The correlation coefficient, often represented by 'r', is a statistical measure that calculates the strength of the relationship between the relative movements of two variables. The values range between -1.0 and 1.0. A correlation of -1.0 shows a perfect negative correlation, while a correlation of 1.0 shows a perfect positive correlation. A correlation of 0.0 shows no linear relationship between the movement of the two variables.
Step 3 ：We can create two lists, one for time and one for percent of chlorine remaining, and then use the correlation coefficient formula to find the correlation coefficient.
Step 4 ：Let's denote the time as \( t = [1, 2, 3, 4, 5, 6] \) and the percent of chlorine remaining as \( c = [84.7, 70.7, 65.6, 47.2, 32.2, 20.5] \).
Step 5 ：By calculating, we find that the correlation coefficient \( r = -0.992992922715922 \).
Step 6 ：Rounding to the nearest thousandth, we get the final answer: The correlation coefficient between time and percent of chlorine remaining is \( r = \boxed{-0.993} \).
