There is no data set for this problem. A researcher is evaluating ways to reduce

Question

There is no data set for this problem.

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. 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 A major goal of the study is to investigate the effect of adding material to the soil on erosion. Write down the coefficients for the linear combination of means which estimates this effect. It should be clear in your answer which coefficients correspond to which treatment means. Is the linear combination in (2b) a contrast? Explain why or why not. A second goal is to see if there are any differences between the three sewage sludge treatments. This question can be answered by comparing two models. Using words or symbols (mu's with subscripts), please describe the two models: full model: reduced model: List the number of error degrees of freedom for each of the models in (2d).

Explanation / Answer

Soil erosion = + B1µ1 + B2µ2 + B3µ3 +B4µ4 +B5µ5 +ei

B1 – Coefficient corresponding to the first treatment i.e nothing is added to the soil

B2 – Coefficient corresponding to the second treatment i.e topsoil is added to the soil

B3 – Coefficient corresponding to the third treatment i.e composite sewage sludge from Cedar Rapids added

B4 – Coefficient corresponding to the fourth treatment i.e composite sewage sludge from Dubuque added.

B5 – Coefficient corresponding to the fifth treatment i.e composite sewage sludge from Des Moines added

µi- the mean corresponding to the ith treatment.

3. No the linear combination is not constant because the mean effects are calculated based on samples and thus, might give different results every time the experiment is conducted.

4.The full model specifies that each of the treatment group will have some mean µi . These means can take any value without any restrictions. When our null hypothesis is true a simpler model can me developed where all the means equal to some value say µ. This common value can take any value, but the main highlight is that the group mean is equal to some value µ. The reduced model is a special case of the full model when our null hypothesis is true. That is if the null hypothesis is proved to be true then, our reduced model will hold. Then we estimate the mean for the group i by the mean of all the observations because all the observation come from a single population with some mean µ when the reduced model holds.

Full model: Soil erosion = + B3µ3 +B4µ4 +B5µ5 +ei

Reduced model: Soil erosion = + Bµ +ei

5.Degrees of freedom for the full model =no. of independent variables= 3

Degrees of freedom of the restricted model = no.of independent variables = 1

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.