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
Write an augmented matrix and use elementary row operations in order to solve the following system of equations. Your final matrix should be in reduced row echelon form. In order to get credit you will have to have a correct final answer as accurate steps in each row operation. (x - 5y = 7) (5x + 8y = -4) Write the augmented matrix: [ ][ ][ ] [ ][ ][ ]
failedAnswered
Write the standard form of the equation of the circle with the given center and radius. Center (-2,2), r=sqrt(3) The equation of the circle in standard form is (Simplify your answer.)
failedAnswered
Q2.3. What is described by the movement of people between compartments in the SIR model? Change in location Change in health status Change in risk of infection
failedAnswered
(75xy)(5x^2y^-5)^2
failedAnswered
A computer manufacturer estimates that its cheapest screens will last less than 2.8 years. A random sample of 61 of these screens has a mean life of 2.5 years. The population is normally distributed with a population standard deviation of 0.88 years. At a=0.02, can you support the organization's claim using the p-value?