48. The catch basin in a storm sewer system is the interface between surface runoff and the sewer. The catch basin insert is a device for retrofitting catch basins to improve pollutant removal properties. The article “An Evaluation of the Urban Stormwater Pollutant Removal Efficiency of Catch Basin Inserts” (Water Envir. Res., 2005: 500–510) reported on tests of various inserts under controlled conditions for which inflow is close to what can be expected in the field.

Consider the following data, read from a graph in the article, for one particular type of insert on x
amount filtered

(1000s of liters) and y
% total suspended solids removed.

Summary quantities are

xi
1251,
x 2 i
199,365,
yi
250.6,
y 2 i
9249.36,

xi yi
21,904.4

a. Does a scatter plot support the choice of the simple linear regression model? Explain.

b. Obtain the equation of the least squares line.

c. What proportion of observed variation in % removed can be attributed to the model relationship?

d. Does the simple linear regression model specify a useful relationship? Carry out an appropriate test of hypotheses using a significance level of .05.

e. Is there strong evidence for concluding that there is at least a 2% decrease in true average suspended solid removal associated with a 10,000 liter increase in the amount filtered? Test appropriate hypotheses using 
.05.

f. Calculate an interpret a 95% CI for true average %

removed when amount filtered is 100,000 liters. How does this interval compare in width to a CI when amount filtered is 200,000 liters?

g. Calculate and interpret a 95% PI for % removed when amount filtered is 100,000 liters. How does this interval compare in width to the CI calculated in

(f) and to a PI when amount filtered is 200,000 liters?