Making Inferences and Justifying Conclusions: Statistics as a Process of Making Inferences (CCSS.S-IC.1)
Common Core High School Statistics And Probability · Learn by Concept
Help Questions
Common Core High School Statistics And Probability › Making Inferences and Justifying Conclusions: Statistics as a Process of Making Inferences (CCSS.S-IC.1)
Researchers contact 200 teens to estimate average screen time for all teens in a city. They cannot survey every teen in the city.
Which statement correctly distinguishes a sample from a population?
A population must be smaller than any sample drawn from it.
A sample contains everyone in the city, while the population is only the 200 teens.
A sample and population are the same when the sample is random.
A sample is the 200 teens surveyed; the population is all teens in the city.
Explanation
The 200 teens are a subset (sample); all teens in the city form the population.
A school polls 100 students about lunch options instead of asking every student. The goal is to learn what the whole school prefers.
Which statement correctly distinguishes a sample from a population?
A sample includes every student, and a population is only a few chosen students.
A sample is the entire school, and a population is the 100 students polled.
A sample is a subset of students selected from the school, and the population is all students in the school.
A sample always gives the exact same result as surveying everyone.
Explanation
The sample is the smaller subset (the 100 students), and the population is the entire group of interest (all students).
A company wants to know the proportion of customers who like a new logo. They randomly contact 500 customers from their entire customer list.
Which statement correctly distinguishes a sample from a population?
All customers are the sample; the 500 contacted customers are the population.
A sample must include every customer to be valid.
The 500 contacted customers are the sample; all customers are the population.
Samples and populations are unrelated.
Explanation
The 500 contacted customers are a subset (sample) of the entire group of customers (population).
A school district wants to estimate the average number of books read per year by its students. They select a random set of 12 schools rather than studying every school.
Why do we study samples instead of entire populations?
Because samples and populations are identical.
Because a sample is the whole group and a population is a part.
Because results from a sample are guaranteed to be perfect.
Because studying a sample is more practical and still gives reliable estimates when chosen randomly.
Explanation
Sampling saves time and resources, and random samples can provide trustworthy estimates of the population.
A principal wants to know the average commute time for students. Instead of asking every student, a random group of 150 students is polled.
Why do we study samples instead of entire populations?
Because samples are guaranteed to give the exact value every time.
Because samples are faster and cheaper while still providing good estimates when random.
Because the population is always too small to measure.
Because populations and samples mean the same thing.
Explanation
Sampling is more practical in time and cost, and a well-chosen random sample can yield reliable estimates of the population.
A factory tests a few items from each batch to estimate the defect rate for all items produced. Testing every item would be costly.
Why do we study samples instead of entire populations?
Because sampling guarantees zero error in estimates.
Because testing a small, random set is more feasible and can provide reliable estimates for the whole output.
Because populations do not have parameters to estimate.
Because samples are more important than populations.
Explanation
Sampling is more feasible in time and cost, and a random sample supports reliable inference about the population.
A produce manager weighs a few crates from a truck to estimate the total weight of all apples. Measuring every apple would take too long.
Why do we study samples instead of entire populations?
Because weighing a subset saves time and resources while still allowing inferences about the whole load.
Because samples are always more accurate than measuring everything.
Because the population is unimportant once a sample is chosen.
Because laws prohibit measuring an entire truckload.
Explanation
Sampling is practical and efficient; a well-chosen random sample can inform us about the whole population.
A city wants to estimate the average time teens spend on social media. Researchers survey 200 teens out of all teens in the city.
Which statement correctly distinguishes a sample from a population?
The 200 surveyed teens are the sample; all teens in the city are the population.
All teens in the city are the sample; the 200 surveyed teens are the population.
The sample and population are always the same group.
A sample must include everyone to be accurate.
Explanation
A sample is a subset of the whole group (population); here, 200 surveyed teens are a subset of all teens in the city.
A health department wants to know the average number of hours teens sleep on school nights. They randomly select 250 teens to survey.
Which statement correctly distinguishes a sample from a population?
The 250 surveyed teens are the sample; all teens in the region are the population.
All teens in the region are the sample; the 250 surveyed teens are the population.
A sample is always exact, so the population is unnecessary.
Samples are used only when the population does not exist.
Explanation
The surveyed 250 teens form a subset (sample) of the entire group of teens in the region (population).
Librarians survey 150 visitors to learn what all library visitors prefer to read. They do not reach every visitor.
Which statement correctly distinguishes a sample from a population?
The population is the 150 visitors, and the sample is everyone who uses the library.
The sample and population must be identical to make inferences.
The sample is the 150 surveyed visitors, and the population is all visitors to the library.
The sample is always exact, so we never need to survey more people.
Explanation
The sample is the surveyed subset; the population is the entire group of interest (all visitors).