Aresearcher wants to determine if extra homework problems 8th grade students learn algebra. one 8th grade class has extra homework problems and another 8th grade class does not. after 2 weeks, the both classes take an algebra test and the results of the two groups are compared. to be a valid matched pair test, what should the researcher consider in creating the two groups?

The two groups must be as similar as possible. They should be demographically homogeneous and have similar academic performance so as the only variable that is different is the one is tested (extra homework assigned)

Step-by-step explanation:

In this case the scientific method is using an experimental group (the 8th grade class that has extra homework problems) and a control group (the 8th grade class that has not extra homework problems) in order to prove if extra homework helps students learn algebra.

In order to be a valid experiments the two groups should present exactly the same characteristics, except for the variable studied, so they must be as homogeneous as possible.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4