XR20-39 Maintaining swimming pools can be quite costly due to all the chlorine that is needed to…

XR20-39 Maintaining swimming pools can be
quite costly due to all the chlorine that is needed to keep the water clear and
relatively free of germs. A chain of hotels (all with outdoor pools) seeking to
reduce costs decided to analyse the factors that determine how much chlorine is
needed.

They commissioned a chemist to conduct an
analysis. It is believed that the speed at which chlorine in a pool is depleted
is dependent on the temperature of the water (higher temperature uses chlorine
faster); pH level, which is a measure of the acidity of the water (pH ranges
from 0 to 14, where 0 is
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XR20-39 Maintaining swimming pools can be
quite costly due to all the chlorine that is needed to keep the water clear and
relatively free of germs. A chain of hotels (all with outdoor pools) seeking to
reduce costs decided to analyse the factors that determine how much chlorine is
needed.

They commissioned a chemist to conduct an
analysis. It is believed that the speed at which chlorine in a pool is depleted
is dependent on the temperature of the water (higher temperature uses chlorine
faster); pH level, which is a measure of the acidity of the water (pH ranges
from 0 to 14, where 0 is very acidic and 14 is very alkaline; levels around 7.5
use the least chlorine); and weather (sunshine uses up chlorine). The chemist
conducted the following experiment. The percentage of chlorine depletion during
8-hour days was recorded under varying conditions of pH level, water
temperature and weather conditions. These data were recorded in the following
way:

Column 1: Percentage of chlorine depletion
over 8 hours

Column 2: Temperature (°C)

Column 3: pH level

Column 4: 1 = mainly cloudy; 2 = sunny; 3 =
partly sunny

a Write the equation of the model that you
would suggest.

b Use regression analysis to estimate the
model’s coefficients.

c Test to determine that the model is
valid.

d Can we infer that higher temperatures
deplete chlorine more quickly?

e Is there evidence to infer that the
belief about the relationship between chlorine depletion and pH level is
correct?

f Can we infer that weather is a factor in
chlorine depletion?

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