A researcher is evaluating ways to reduce erosion from freew

A researcher is evaluating ways to reduce erosion from freeway roadsides by adding material to the soil along the roadside. 20 plots on a newly built roadside were randomly assigned to one of 5 treatments (listed below). Grass was seeded into all plots in the spring. In late summer, the amount of soil erosion (grams of soil eroded) was measured on all plots. The treatments were: 1) control, nothing added, 2) topsoil added 3) composted sewage sludge from Cedar Rapids added, 4) composted sewage sludge from Dubuque added, 5) composted sewage sludge from Des Moines added.
A One-way Analysis of Variance was used to analyze these data.
(a) The p-value from the F-test that compares the equal means model to the separate means model is 0.021. Carefully state an appropriate conclusion from this test, in the context of the study.
(b) A major goal of the study is to investigate the eect of adding material to the soil on erosion. Write down the coecients for the linear combination of means which estimates this eect. It should be clear in your answer which coecients correspond to which treatment means.

Solution