1

Problem

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 significantly improved accuracy when adding fractions. What is the largest group to which the study results can be generalized?

2

Step

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.

3

Step

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.

4

Step

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.

5

Step

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.

6

Solution

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

7

Sumup

Please summarize steps

Choices

8

Choice-A

This sample size is limited. While the study focused on 35 students, it’s not accurate to assume only they would benefit from the educational game. The sample aims to represent a broader population

Wrong The 35 students in the sample.

9

Choice-B

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

Correct All students at the school.

10

Choice-C

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

Wrong All middle school students in the city.

11

Choice-D

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

Wrong All students in the city.

12

Answer

Option

B

13

Sumup

Please summarize choices