A psychologist designed and conducted a study to determine whether playing a certain educational game increases middle school students accuracy in adding fractions. For the study, the psychologist chose a random sample of 35 students from all of the students at one of the middle schools in a large city. The psychologist found that students who played the game showed significant improvement in accuracy when adding fractions. What is the largest group to which the results of the study can be generalized?

Sample Size:
→ The study used 35 students, a small sample. Generalizing to the entire school (a larger but defined group) is a safer bet than a much larger and more diverse population like all middle schoolers in the city or the entire city’s students

Shared Characteristics
→ Students within the same school likely share similar educational backgrounds, age, and potentially socioeconomic factors. This increases the chance the game would affect all students at the school similarly compared to students across the city with potentially wider variations

However, there are limitations to consider:
School Specificity:
→ The school environment itself might influence the results. Maybe the teachers or curriculum play a role. Generalizing to all schools needs caution

Random Sample:
→ Even within the school, the selected 35 students may not perfectly represent the entire population. Ideally, the sample selection should be random to minimize bias

Therefore, "All students at the school" allows some level of generalization, it’s important to acknowledge these limitations when interpreting the study’s findings.

This option is too narrow. While the study was conducted on these 35 students, it would be overly restrictive to conclude that only these 35 students would benefit from playing the educational game. The sample is meant to represent a larger group

The 35 students in the sample

This is the correct option. Since the 35 students were randomly selected from all the students at the middle school, the results of the study can be generalized to all students at that school. Random sampling ensures that the sample is representative of the larger group within the school

All students at the school

This option is wrong because the study only involved students from one middle school. Without including students from multiple schools across the city, there’s no statistical basis to generalize the results to all middle school students in the city

All middle school students in the city

This option is incorrect. The study focused specifically on middle school students and did not include students from other educational levels (e.g., elementary or high school students). Therefore, the results cannot be generalized to all students in the city

All students in the city

Option

B

Can you summarize what you’ve understood in the above steps?