It is important to determine if generalizations are valid. We can consider the following two things:
Was the sample random? Did all members of the population have an equal chance of being selected?
Is the sample size large enough based on the population size?
(3 points)
Valid Invalid
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.
Invalid - The sample is not random and the sample size is too small compared to the population size.
Invalid - The sample is not random and is not representative of the entire population.
Valid - The sample is random and the sample size is sufficient based on the population size.
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
The first scenario is valid because the sample is random and the sample size is sufficiently large.
The second scenario is invalid because the sample is not random and is biased by only asking Jorge's friends.
The third scenario is invalid because the sample is random but the sample size is too small compared to the population size.
Therefore, the correct answer is: valid, invalid, invalid.
which goes with valid and what goes with invalid
Apologies for any confusion earlier. Let's clarify:
In the given scenarios:
1. The principal at a middle school wanting to know the average number of clubs students participate in and using a random sample of 100 students is considered valid because the sample is random and the sample size is sufficient.
2. Jorge asking his 5 friends about attendance at the basketball game and then concluding that all students will attend is considered invalid because the sample is too small and biased.
3. Nick putting all student names in a box, drawing 100 names, and determining that soccer is the most popular sport is considered invalid because while the sample is random, the sample size is too small for a population of 500 students.
So, in summary:
- The first scenario is "valid."
- The second and third scenarios are "invalid."