Question

1. An experiment is to be conducted to assess effect of temperature on the
amount of impurities removed by using water samples contaminated with the
same level of impurity. Six samples are to be tested at each of 5 temperatures
and the amount of impurities removed in each sample recorded.
(a) What is the response variable?
(b) What is the factor of interest?
(c) What are the levels of this factor?
(d) What experimental design is suitable?
(e) Describe how the 30 measurements should be made.
(f) If the samples did not have the same level of impurity, what response variable
will be appropriate?
(g) Why is using samples with the same level of impurity better?
(h) Write the appropriate model for this experiment. Define the terms in the model
with reference to this experiment.

Answer 1

a) Six samples with same level of impurities were taken for testing. Since the impurities are at the same level we say that homogeneous treatment units are considered for testing. The response variable is the amount of impurities removed.

b) The factor of interest is the temperature which has 5 levels.

c) The levels are the 5 different temperatures.

d) Since the treatment units have the same level of impurity ( homogeneous) we can apply a completely randomised design. Here we have 5 different temperatures with 6 replications, so in total there are 5*6=30 experimental units . Here none of samples receive the same treatment\

e) Each sample undergoes 5 different temperatures and the impurties removed in each temperature is noted Hence we have 5 different impurity measurements for each sample of water. Since we have six repetitions of the above experiment We will have 5*6=30 impurity measurements.