A Researcher Is Studying the Effects of Learning a Problem-Solving

A researcher is studying the effects of learning a problem-solving strategy upon the mathematics achievement of sixth- grade students. He selects a sample of students in one school and randomly assigns half of them to the experimental group and half to the control group. All students will be given a pretest of mathematics achievement. The experimental group then will receive a one-hour lesson that teaches a problem-solving strategy for students to use in solving word problems in mathematics. The control group receives conventional instruction. Because he expects the problem-solving training to work best with the brighter students, the researcher divides both groups into two subgroups based on their IQ scores, using the following categories: below 90, 90-110, 111-130, and above 130. He administers a mathematics achievement posttest to all research participants two months after the treatment ends. Explain why a fairly large sample size is required for this project.