Marcus wants to predict the next student council president. He polls every fourth person from each grade level as they exit the cafeteria. In his poll, 65% chose Sophia. What type of sample was taken? Can his result be extended to the rest of the school?
sample was systematic. Systematic sampling is easier to do than random sampling. In systematic sampling, the list of elements is "counted off". That is, every kth element is taken. This is similar to lining everyone up and numbering off "1,2,3,4; 1,2,3,4; etc". When done numbering, all people numbered 4 would be used.
Since the sample was uniform over the school, it can be used.
The type of sample taken by Marcus is called a systematic sample. He is polling every fourth person from each grade level.
However, based on the information provided, it is not possible to determine whether his results can be extended to the rest of the school. This is because the sample may not be representative of the entire student population. For example, if there is a specific pattern or bias in the selection of every fourth person, it may not accurately reflect the preferences of the entire student body. In order to generalize the results to the rest of the school, a random and representative sample would be more appropriate.
The type of sample that Marcus took is called a systematic sample. He polled every fourth person from each grade level, meaning that he applied a predetermined pattern to select his participants.
As for whether his result can be extended to the rest of the school, it depends on the representativeness of his sample. In this case, Marcus only polled every fourth person from each grade level, which introduces the potential for sampling bias. For example, if the cafeteria had a seating arrangement where students from certain grades were more likely to sit closer to the exit, then Marcus's sample may not accurately reflect the entire school's population.
To ensure that Marcus's result can be extended to the entire school, he would need to use a random sampling method. Random sampling involves selecting individuals from the population in a way that gives every member an equal chance of being included in the sample. By using a random sample, Marcus can minimize the risk of sampling bias and increase the generalizability of his results to the entire school population.