Question

In preparing for a test on a set of material, is it better to study one topic at a time or to study topics mixed together? In one study,¹ a sample of fourth graders were taught four equations. Half of the children learned by studying repeated examples of one equation at a time, while the other half studied mixed problem sets that included examples of all four types of calculations grouped together. A day later, all the students were given a test on the material. The students in the mixed practice group had an average grade of 77, while the students in the one-at-a-time group had an average grade of 38. What is the best estimate for the difference in the average grade between fourth-grade students who study mixed problems and those who study each equation independently?

a) Give the notation (as a difference with a minus sign) for the quantity we are trying to estimate.

Let group 1 be the fourth-grade students who study mixed problems and let group 2 be the fourth-grade students who study each equation independently.

b) Give the notation for the quantity that gives the best estimate.

Let group 1 be the fourth-grade students who study mixed problems and let group 2 be the fourth-grade students who study each equation independently.

c) Give the value of the best estimate.

Answer 1

(a)

The notation for the quantity we are trying to estimate:

where is the population mean for the fourth- grade students who study mixed problems

is the population mean for the fourth- grade students who study each equation separately.

(b)

The notation for the quantity that gives the best estimate:

where is the Sample mean for the fourth- grade students who study mixed problems

is the Sample mean for the fourth- grade students who study each equation separately.

(c)

Value of the best estimate:

77 - 38 = 39

So,

Answer is:

39