Question

A researcher is interested in determining whether the average size of coffee particles remaining in a coffee filter after brewing differ between two filter materials. The researcher plans to conduct an experiment using 10 tablespoons of dry coffee and 4 cups of water for every experimental run. The experimenter plans to run 5 filters of type A and 5 filters of type B. The order of the filters will be randomized.

a. Which variable would be considered an explanatory variable; which variable would be considered an outcome variable. Justify why.

b. Write a terms formula that would be useful for representing this research question. Use simplified names of the variables for the terms formula.

Answer 1

(a)

Explanatory variable: filter type, Outcome variable: the average size of coffee particles

(b)

$Let~y_i=the average size of coffee particles~after~ith~brewing\\ x_i=1~if~we~use~Type~A~filter\\ =0~if~we~use~Type~B~filter\\ Then~model~is\\ y_i=\alpha+\beta x_i+e_i\\ e_i=random~error\\ \alpha=intercept\\ \beta=slope$