Exploring Random Sampling and Population Inferences

This lesson covers random sampling and population inferences. It explains how to determine if a sample is random and how to make inferences about a population based on sample data. The lesson includes scenarios to evaluate randomness and uses proportions to predict outcomes in a larger population. Students learn to analyze survey data and make informed predictions.

What is a necessary condition for a sample to be considered random?

• Only specific groups are surveyed

• Participants are chosen by a specific person

• Everyone has an equal chance of being selected

• Only volunteers are included

Why is a survey of only choir members not a random sample?

• All students have an equal chance

• It randomly selects students from the choir

• Only choir members are surveyed

• It includes all school members

What method ensures a random sample from the senior class?

• Choosing students who volunteer

• Surveying only bus riders

• Randomly selecting numbers assigned to each senior

• Asking teachers to select students

What is the purpose of setting up a proportion in population inferences?

• To select the best students

• To compare different populations

• To ensure the sample is random

• To predict outcomes based on the sample

How many students were surveyed in the elective preference example?

• 30 students

• 60 students

• 40 students

• 50 students

What percentage of surveyed students chose Spanish as their elective?

• 45%

• 25%

• 55%

• 35%

Using the sample, how many students can be expected to sign up for Art?

• 60 students

• 45 students

• 53 students

• 70 students

If less than 10% of the population signs up for an elective, it will be dropped. Should Art be dropped based on the sample?

• No, because more than 10% of the sample chose Art

• Yes, because less than 10% signed up

• Yes, because exactly 10% signed up

• No, because exactly 10% signed up

What can be inferred if over half of the sample chooses Theater?

• More than half of the population will choose Theater

• Less than half of the total population will choose Theater

• None of the above

• Exactly half of the population will choose Theater

Is the statement 'At least 120 students will sign up for Spanish' true based on the sample?

• True, as the proportion predicts more than 120

• False, as the proportion predicts less than 120

• True, as exactly 120 students will sign up

• False, as no predictions can be made from the sample