48. The catch basin in a storm sewer system is the interface between surface runoff and the...
Question:
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?
Step by Step Answer:
Probability And Statistics For Engineering And The Sciences
ISBN: 9781111802325
7th Edition
Authors: Dave Ellis, Jay L Devore