Question bank: Census and Sample Research

The school XYZ is interested in knowing the students' opinion about the quality of the food served in the cafeteria. Since there are 1,500 students in the school, the committee decided to conduct a survey to collect the necessary information. What is the most suitable research method for this case and how many students should be interviewed, considering the need for representativeness and saving time and resources?

During an interdisciplinary class that addressed notions of statistics and geography, 7th-grade students were challenged to plan a survey to determine the most used means of transportation by the inhabitants of their city on the daily route from home to school. Considering the acquired knowledge about census and sample surveys, the students thought about conducting an exhaustive count in a total of 40 blocks in a central region of the city, where both low-income families, who usually use public transportation, and high-income families, who tend to use private vehicles, reside. Based on the study's guidelines, the students decided that the survey should be representative and capable of offering results that could be generalized to the entire population of the city without the need to cover all its inhabitants. In this scenario, which type of survey (census or sample) should the students choose to achieve their objectives and why?

In a study on the reading habits of students at a school, a researcher wants to collect data to analyze the reading preferences of 7th-grade students. The researcher can choose to conduct a census survey, where all 7th-grade students will be interviewed, or a sample survey, where a representative sample of this group will be selected for the interview. Considering that the census survey can be more time-consuming and costly, while the sample survey may have results with a margin of error, discuss which method would be more appropriate for this study. Additionally, explain the possible consequences of choosing the research method on the interpretation of results and the formulation of conclusions about the reading habits of 7th-grade students.

In the graph below are represented the results of a sample survey on the fuels used in cars in a certain city. What is the most preferred fuel in this city?

A school wishes to conduct a survey to understand the profile of students who would benefit the most from Math reinforcement classes. The board is considering two approaches: a census survey, which would involve evaluating all 7th grade students, and a sample survey, which would involve only a portion of the students. The 7th grade has 6 classes with 35 students each. To decide which approach is more suitable, the school needs to consider the efficiency of time and resources and the representativeness of the results. If opting for the sample approach, the school intends to choose a sample that is representative of all classes. Considering that the school can choose up to 4 classes for the sample, elaborate a plan explaining: 1) Why a census survey may be more appropriate in certain contexts and 2) How the school could select a representative sample, justifying the choice of classes and the selection methods.