Mr. Moore is installing new work benches in the wood shop. He wants the height of the benches to be best for students standing and working on projects. He decides to use the mean height of the students in the school as a guide. The school has 6th, 7th, and 8th grade students. Rather than using the heights of all the students in the school, he decides to take a sample of students.
Suppose Mr. Moore decides to use 20 seventh graders as the sample. Is this sample a random sample? Explain your reasoning.
Mr. Moore decides to use a random number generator to select 20 students from the school. Suppose that when choosing 20 students using the random generator on the graphing calculator, Mr. Moore’s sample is all eighth graders. Does that mean the sample is not a random sample? Explain your reasoning.
If Mr. Moore uses 20 seventh graders as the sample, it is not a random sample because it only includes students from one grade level, whereas the population he's trying to estimate the mean height for includes students from all three grade levels (6th, 7th, and 8th grades). This sample is biased towards the seventh graders' heights and may not be representative enough of the entire school population.
If Mr. Moore uses a random number generator to select 20 students from the school and all the selected students happen to be eighth graders, this sample can still be considered as a random sample. This is because the selection process was random, even though it resulted in a sample comprising of students from just one grade level. However, it's important to note that while the sample is random, it may not be as representative of the entire population as a sample containing students from all three grade levels. The chances of obtaining a more balanced sample across grades would likely improve by increasing the sample size or implementing a stratified random sampling approach.