Questions: Keeping water clean. Keeping water supplies clean requires regular measurement of levels of pollutants. The measurements are indirect - a typical analysis involves forming a dye by a chemical reaction with the dissolved pollutant, then passing light through the solution and measuring its "absorbance." To calibrate such measurements, the laboratory measures known standard solutions and uses regression to relate absorbance and pollutant concentration. This is usually done every day. Here is one series of data on the absorbance for different levels of nitrates. Nitrates are measured in milligrams per liter of water. Nitrates: 50, 50, 100, 200, 400, 800, 1200, 1600, 2000, 2000. Absorbance: 7.0, 7.5, 12.8, 24.0, 47.0, 93.0, 138.0, 183.0, 230.0, 226.0. a. Chemical theory says that these data should lie on a straight line. If the correlation is not at least 0.997, something went wrong, and the calibration procedure is repeated. Plot the data and find the correlation. Must the calibration be done again? b. The calibration process sets nitrate level and measures absorbance. Once established, the linear relationship will be used to estimate the nitrate level in water from a measurement of absorbance. What is the equation of the line used for estimation? What is the estimated nitrate level in a water specimen with absorbance 40? c. Do you expect estimates of nitrate level from absorbance to be highly accurate? Why?

Keeping water clean. Keeping water supplies clean requires regular measurement of levels of pollutants. The measurements are indirect - a typical analysis involves forming a dye by a chemical reaction with the dissolved pollutant, then passing light through the solution and measuring its "absorbance." To calibrate such measurements, the laboratory measures known standard solutions and uses regression to relate absorbance and pollutant concentration. This is usually done every day. Here is one series of data on the absorbance for different levels of nitrates. Nitrates are measured in milligrams per liter of water. Nitrates: 50, 50, 100, 200, 400, 800, 1200, 1600, 2000, 2000. Absorbance: 7.0, 7.5, 12.8, 24.0, 47.0, 93.0, 138.0, 183.0, 230.0, 226.0. a. Chemical theory says that these data should lie on a straight line. If the correlation is not at least 0.997, something went wrong, and the calibration procedure is repeated. Plot the data and find the correlation. Must the calibration be done again? b. The calibration process sets nitrate level and measures absorbance. Once established, the linear relationship will be used to estimate the nitrate level in water from a measurement of absorbance. What is the equation of the line used for estimation? What is the estimated nitrate level in a water specimen with absorbance 40? c. Do you expect estimates of nitrate level from absorbance to be highly accurate? Why?
Transcript text: Keeping water clean. Keeping water supplies clean requires regular measurement of levels of pollutants. The measurements are indirect - a typical analysis involves forming a dye by a chemical reaction with the dissolved pollutant, then passing light through the solution and measuring its "absorbance." To calibrate such measurements, the laboratory measures known standard solutions and uses regression to relate absorbance and pollutant concentration. This is usually done every day. Here is one series of data on the absorbance for different levels of nitrates. Nitrates are measured in milligrams per liter of water. \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline Nitrates & 50 & 50 & 100 & 200 & 400 & 800 & 1200 & 1600 & 2000 & 2000 \\ \hline Absorbance & 7.0 & 7.5 & 12.8 & 24.0 & 47.0 & 93.0 & 138.0 & 183.0 & 230.0 & 226.0 \\ \hline \end{tabular} a. Chemical theory says that these data should lie on a straight line. If the correlation is not at least 0.997 , something went wrong, and the calibration procedure is repeated. Plot the data and find the correlation. Must the calibration be done again? b. The calibration process sets nitrate level and measures absorbance. Once established, the linear relationship will be used to estimate the nitrate level in water from a measurement of absorbance. What is the equation of the line used for estimation? What is the estimated nitrate level in a water specimen with absorbance 40 ? c. Do you expect estimates of nitrate level from absorbance to be highly accurate? Why?
failed

Solution

failed
failed

Solution Steps

Step 1: Collect Data

Collected nitrate concentration data: [50, 50, 1, 200, 400, 800, 1200, 1600, 2000, 2000] Collected absorbance data: [7, 7.5, 12.8, 24, 47, 93, 138, 183, 230, 226]

Step 2: Compute the Correlation Coefficient (r)

Using the formula: $$ r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}} $$ Substituting the values, we get: r = 1

Step 3: Evaluate the Correlation

The computed correlation coefficient r = 1 Since r >= 0.997, the calibration is considered valid.

Final Answer:

The correlation coefficient between nitrate concentration and absorbance is 1, which is considered valid based on the threshold of 0.997.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Determine whether the quantitative variable is discrete or continuous. Number of notes in a song Is the variable discrete or continuous? A. The variable is continuous because it is countable. B. The variable is discrete because it is countable. C. The variable is discrete because it is not countable. D. The variable is continuous because it is not countable.
failedAnswered
Find the length and direction (when defined) of u × v and v × u. u = -4i - 4j - 6k, v = 5i + 5j + 3k
failedAnswered
What is #5 pointing to? parathyroid fluid thyroid fluid colloid region thyroid cells
failedAnswered
18. Points A and B, are shown in the figure below within a 3D Cartesian coordinate system. Point B is located on the y-z plane. Answer the following questions. (a) Write a Cartesian position vector representing the position of point A with respect to point B. (b) Calculate the distance between the two points.
failedAnswered
Una máquina produce componentes que son defectuosos en un 10%. Se elige al azar una muestra de estos 50 componentes, calcula: a) La probabilidad de que existan 3 o más componentes defectuosos. b) El número esperado de componentes defectuosos.