It is important to determine if generalizations are valid. We can consider the following two things:
1. Was the sample random? Did all members of the population have an equal chance of being selected?
2. Is the sample size large enough based on the population size?
(3 points)
The principal at a middle school wants to know the average number of clubs students participate
in. She uses a random number generator from 0-500 representing all students. She chooses
100 numbers at random and surveys these students. She concludes that students participate on
average in 2 clubs each.
Jorge wants to know how many students in his school are going to the basketball game. Jorge
asks 5 of his friends, and all of them say they are going. He concludes that all students will
attend the basketball game.
Nick wants to determine the most popular sport in his school of 500 students. He puts the names
of all the students in the box, draws 100 of them, and surveys them all. He determines that
soccer is the most popular sport in the school.
Valid
Invalid
Invalid
1. The principal's sample is random and the sample size seems appropriate for the population size. However, without knowing if the numbers chosen represent all students in the school, the generalization may not be valid.
2. Jorge's sample size is too small to make a generalization about all students attending the basketball game.
3. Nick's sample is random and the sample size seems appropriate, but without considering the entire population, the generalization that soccer is the most popular sport in the school may not be valid.