#238 Laboratory experiments designed to measure

Laboratory experiments designed to measure - Math

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Free Chegg Question

Laboratory experiments designed to measure LC50 (lethal concentration killing 50%of the test species) values for the effect of certain toxicants on fish are run by two different methods. One method has water continuously flowing through laboratory tanks, and the other method has static water conditions. For purposes of establishing criteria for toxicants, the Environmental Protection Agency (EPA) wants to adjust all results to the flow-through condition. Thus, a model is needed to relate the two types of observations. Observations on toxicants examined under both static and flow-through conditions yielded the data in the accompanying table (measurements in parts per million, ppm). Fit the model Y = β₀ + β₁ x + ε.

What interpretation can you give to the results?

b Estimate the flow-through value for a toxicant with an LC50 static value of x = 12 ppm.

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Free Chegg Answer

1. Step 1 of 8

   To fit the model to the given data.

   Here  is the random error component with.

2. Step 2 of 8

   The least squares estimates of the coefficients  and, say, and, given by

   

   

   

   where,  and 

3. Step 3 of 8

   Consider the following table:

   Table 1: Calculation for finding the coefficients

    

   Toxicant	LC50 Flow-Through ()	LC50 static ()
   1	23.00	39.00	897	1521
   2	22.30	37.50	836.25	1406.25
   3	9.40	22.20	208.68	492.84
   4	9.70	17.50	169.75	306.25
   5	0.15	0.64	0.096	0.4096
   6	0.28	0.45	0.126	0.2025
   7	0.75	2.62	1.965	6.8644
   8	0.51	2.36	1.2036	5.5696
   9	18.00	32.00	896	1024
   10	0.39	0.77	0.3003	0.5929
   Total

4. Step 4 of 8

   Clearly, from the above table, we have

   ,

   ,

   ,

   

   

   

   

   

   

   

5. Step 5 of 8

   

   

   

   

   

   

   Therefore, the fitted model is 

6. Step 6 of 8

   (a) The fitted regression (linear) model indicates that the change in the predicted value of LS50 flow-through will increase 0.66 units for a unit increment in LC50 static value and will be -0.78 if all the LC50 static values are zero.

7. Step 7 of 8

   (b) The estimator of the flow-through value for a toxicant with an LC50 static value of  is 

8. Step 8 of 8