Question

tiana is in 7th grade and wants to determine if the other students in her school would like to have more variety in their cafeteria lunches. surveying a random sample of 7th graders, she finds that 90% of them would like more variety in their cafeteria lunches. she then goes to the city’s library and asks people there if the school should have more variety in their lunches. of those surveyed, 24% of the people said they would like more variety in the cafeteria lunches. explain an error in tiana’s method of surveying two populations to determine if the other students in her school would like to have more variety in their cafeteria lunches?

Explanation:

Step1: Identify the sampling populations

Tiana first surveys 7th - graders (a specific grade in her school) and then surveys people at the city's library (a general population in the city, not limited to her school).

Step2: Analyze the error in sampling

The goal is to determine if other students in her school want more variety in cafeteria lunches. When she surveys people at the city's library, these people are not necessarily students from her school. So, the second population (people at the city's library) is not relevant to the target population (students in her school). This is a sampling error because the sample from the library does not represent the students in her school. The first sample (7th - graders) is a part of the target population (students in her school), but the second sample is from an unrelated population.

Answer:

The error in Tiana's method is that when she surveyed people at the city's library, this population is not composed of students from her school (the target population for her question about cafeteria lunch variety in her school). So, the second sampling population (people at the city's library) is not representative of the students in her school, leading to a sampling error as it does not help answer the question about her school's students' preferences for cafeteria lunch variety.