Determine If a Sample Is Representative of a Population

Lana and Jeff each randomly surveyed 15 students about their favorite types of movies. What would you expect to see in the samples? Select all that apply.

• Different members are found in each sample.

• Some members may possibly overlap in each sample.

• Each sample gave the same responses.

• Both samples could be representative of the population.

• Both samples include only Lana and Jeff's friends.

The principal at Marina Middle School wants to determine if the 120 students in the seventh grade prefer to visit Catalina Island or Camp Mosaic for their end-of-year trip. Which of the following is a representative sample of the population? Select all that apply.

• 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

The city council in Middlefield wants to know if residents are in favor of a traffic camera at the main intersection in town. Which example is likely to produce a representative sample?

• Drivers who reside in Middlefield

• Residents randomly chosen from the town register

• All residents of Middlefield

• All people with a five-letter last name

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?

• Line up the students by height and choose the first 20 students.

• Use the school roster and randomly choose 50 boys.

• Obtain an alphabetized list of all the students in the school and select every seventh student.

• Place all the names of the students in Mrs. Walsh's math class in a hat and randomly select 10 students.

Vanessa’s class is studying the number of car commercials on television between 6 p.m. and 8 p.m. for five days. Which is the best sample for Vanessa to use?

• The commercials between 6 p.m. and 8 p.m. on each day

• The first five commercials each of the five days

• The commercials shown between 6 p.m. and 7 p.m. on a randomly chosen day

• The commercials shown between 6:30 p.m. and 7:30 p.m. on three randomly chosen days

Trevor's science class is studying the rainfall on the first day of each month for one year. Explain why studying the rainfall on the first day of​ September, October, and November is not a random sample.

• These are three consecutive months. The sample should be spread out across the whole year and include more than three months.

• These are three specific months which is too large of a sample to be a random sample.

• The three months mentioned do not count.

• In these three​ months, the rainfall on the first day of the month is too small to measure.

To predict the performance of her first period class on their next quiz, a teacher randomly selects eight students from the class and takes the mean of their scores on the last quiz. Is this sample representative of the​ class's performance on the quiz?

• ​No, because the students were chosen from the best students in the class.

• ​Yes, because the students were chosen based on their class average.

• ​No, because it is a simple random sample.

• ​Yes, because it is a simple random sample.

To try to predict the outcome of the vote for the school board election school board election​, a town manager used random numbers to pick 100 registered voters. She then called these voters and asked how they planned to vote. Is the sample taken in this problem representative of the population?

• No, because it does not contain the same number of subjects as the population.

• ​Yes, because it is a systematic sample.

• ​Yes, because it is a simple random sample.

• ​Yes, because it contains the same number of subjects as the population.

A movie theater considers upgrading to offer luxury seating. The manager randomly surveys​ 1,200 residents who live within 10 miles of the theater. What is the sample in this​ situation?

• The​ 1,200 residents surveyed

• ​1,500 randomly surveyed customers of the movie theater

• All of the movie​ theater's customers

• All residents who live within 10 miles of the theater

You want to study a random sample of 4 out of 26 students in your class. Describe a process you could use to create a random sample with 4 subjects.

• Assign each student a number in alphabetical​ order, then select 4 random numbers.

• Select 4 students who sit close to you.

• Select the 4 students whose names come first alphabetically.

• Assign each student a​ number, then select students 1 through 4.