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.

A. Suppose Mr. Moore decides to use 20 seventh graders as the sample. Is this sample a random sample? Explain your reasoning.

B. 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.

A, Not random if you pick a particular subset

B, Random, but you need a bigger sample.

A. No, the sample of 20 seventh graders is not a random sample. A random sample should be selected in a way that every member of the population has an equal chance of being included in the sample. By specifically choosing only seventh graders, Mr. Moore is not including students from other grades, thereby introducing bias into the sample.

B. Yes, the sample of all eighth graders selected using a random number generator is still a random sample. Random samples can still exhibit unusual or unexpected patterns due to chance. In this case, it is possible that the random number generator happened to select only eighth graders, but it doesn't affect the randomness of the selection process itself. Random samples allow for the possibility of such outcomes, and it is important to note that randomness does not guarantee equal representation of all groups in every individual sample.