Sampling to Draw Inferences About Populations

A theme park has many attractions, one of which is the roller coaster. Are the people who ride the roller coaster the population or a sample of the theme park? Explain.

• Sample. They are a subset of all the people at the theme park.

• Population. They are all the people at the theme park.

The principal at Marina Middle School wants to determine if the 120 students in the seventh grade prefer to visit the aquarium or the science museum for their end-of-year trip. Select all the sets of people that would be a representative (good) sample of the population. (Hint: 2 answers)

• 20 sixth-grade students, 20 seventh-grade students, and 20 eighth-grade students

• 10 seventh-grade boys and 10 seventh-grade girls

• 25 seventh-grade students

• 15 seventh-grade boys and 5 teachers

• 25 students from the school

Students in Mrs. Walsh’s math class wanted to know the favorite snacks of students in the school. How could they generate a random sample to survey?

• The class could obtain an alphabetized list of all of the students in the school and select every seventh student.

• The class could each ask one of their best friends.

• The teacher can choose a sample of students.

• The class could select the first 20 students that visit the school canteen shop.

The food service manager conducted a random survey of students to determine their preference for new lunch menu items. Select all the inferences that can be drawn from the manager’s data. (Hint: There are 3 answers)

• About twice as many students prefer salad bar as compared to pita sandwiches.

• Burritos are the most preferred item.

• About three-fourths of students prefer

  either salad bar or burritos.

• Twice as many students prefer pizza as compared to pita sandwiches.

• About half as many students prefer pita sandwiches as compared to burritos.

True or False: all samples lead to a good prediction about an entire population.

• True

• False

How can sample data be used to form an estimate about the population?

• A proportion can be solved to relate the sample to the population.

• A proportion can be solved to relate the sample to the mean.

• A proportion can be solved to relate the sample to the median.

• You cannot make an estimation from sample data.

A travel club has 3,000 members. A random sample of 50 of the club members found that 12 people like mountain vacations best. Which statement is NOT supported by the sample data?

• Twenty-four percent of those sampled say they like mountain vacations best.

• An estimated 720 club members would likely say they enjoy mountain vacations best.

• Almost one-quarter of club members would likely say they enjoy mountain vacations best.

• More than 2,500 club members would likely say they prefer other vacations over mountain vacations.

What inference can you draw from this survey?

• I can infer that most students in this school like pizza.

• I can infer that very few students like hamburgers.

• I can infer that their favorite is corn dogs.

• I can infer that most students in this school like hamburgers.

Margo wants to convince her father to change her curfew from 9 P.M. to 10 P.M. She gathers data on curfew times from a random sample of students at her middle school. Can Margo use these data to present a valid inference that will convince her father? Explain.

• No. Most students have a curfew of 9 P.M. or earlier.

• Yes. Most students have a curfew of 10 P.M. or earlier.

• Yes. Some students have a curfew of 10 P.M. or later.

Russell randomly surveys seventh-graders in his school and finds that 6 of 30 attend summer camp. If there are 200 seventh-graders in his school, about how many are expected to attend summer camp?

Mathematical Equivalence

ON