Selecting a Cluster Random Sample

  • 1.

    A chain of grocery stores is curious about the brands their customers buy. Describe how a cluster random sample could be selected from their 20 stores.

    Answers:

    • (1) In each store, make a group by selecting every 8th person in the checkout line.

    • (2) Randomly choose a store and select all of the customers in that store.

    • (4) Assign a number to every customer in all stores, then randomize the numbers and use the first 50 people as the sample group.

    • (3) Randomly select a few people from each store.

  • 2.

    A company has offices on 4 floors of a building. The president of the company wants a sample of employees. What is a way they could collect a clustered random sample?

    Answers:

    • Randomly choose some employees from each floor to make the sample.

    • On a list of employees, select every 10th employee to make a sample.

    • Take a list of all of the employees and randomize their names. Make a sample from the first page of this randomized list.

    • Randomly choose one floor and use all of the employees on that floor as the sample.

  • 3.

    An apartment complex has 14 separate buildings. The manager wants a random sample of residents. Which of the following is a description of cluster sampling in this situation?

    Answers:

    • A sample of all residents in one building.

    • A sample made by going to every building and talking to the resident in the first apartment, then every 8th apartment after that.

    • A sample made of all residents who have an apartment number with a 5 in it.

    • A sample of 140 residents, 10 from each building.

  • 4.

    An animal shelter has 8 different animal areas. To analyze the ages of the animals, Jody wants to gather a sample by the cluster method. Select the correct cluster sample from the following options.

    Answers:

    • Select the area with the most animals as the sample.

    • Select several animals from each of the areas to use as the sample.

    • Take an inventory of all of the animals and randomly select a sample from the list.

    • Select one animal area and use all of those animals as the sample.

  • 5.

    All freshman classes have 35 students, and 10 different classes start at noon. The principal wants to use the cluster method to collect a random sample of students. Which of the following best describes the cluster sample in this situation?

    Answers:

    • A cluster sample is 5 students from each of the 10 different classes.

    • A cluster sample is made by selecting all students who play sports.

    • A cluster sample is made from randomizing a list of all 350 students.

    • The cluster sample is all 35 students in one of the 10 different classes.

  • 6.

    Benjamin Building Company is constructing a new neighborhood. The neighborhood is made of 5 different streets, each with 20 houses. What is a way someone could use cluster sampling to select a group of houses?

    Answers:

    • Randomly select one street and use all 20 houses as a sample.

    • Start at the first street and select every 4th house on each street.

    • Select the homes that were built most recently.

    • Randomly select 4 houses on each street to make a sample of 20.

  • 7.

    Ms. Taylor has a list of all of her students, organized alphabetically. Describe a method for her to gather a clustered random sample.

    Answers:

    • Randomly select all of the students who have a last name starting with R.

    • Randomize the list and use the first 10 names on the list as the sample.

    • Start at the top of the list and make a sample of the first student along with every 3rd student after that.

    • Randomly select a few students from all letters of the alphabet.

  • 8.

    While organizing his room, Jon filled a dresser that has 7 different sized drawers. He then wanted to analyze the price of a random sample of items.. Select the best method for him to do this with the cluster random method.

    Answers:

    • Find all of the items that are black.

    • Randomly choose one drawer and look at all items in that drawer.

    • Use the items that he bought most recently.

    • Randomly choose a few items from each of the drawers.

  • 9.

    Robin is collecting information about the age of books in the library. This library has sections for history, mathematics, science, art, and music. Which is the best way to select a sample using the cluster method?

    Answers:

    • Randomly choose one section and look at all of the books in that section.

    • Go through all sections, starting at the first shelf and select every 20th book.

    • Randomly choose 10 books from each of the different sections.

    • Go through all sections and pick any hard-cover books.

  • 10.

    While checking for typos in a textbook, Mary used a cluster random sample. Which of the following is most likely what she did?

    Answers:

    • Randomly select one chapter of the book and look at the whole chapter.

    • Choose all pages that have a number ending in 7.

    • Flip through the pages and randomly pick 200 pages.

    • Randomly select a few sections from each chapter of the book.

  • 11.

    At the grocery store, 13 different types of rice are sold in bins. In an effort to investigate the presence of bacteria in rice, how could someone gather a sample using the cluster random sampling method?

    Answers:

    • Gather some rice from each of the different bins.

    • Use the rice from the bin that is the most full.

    • Use one randomly chosen bin of rice as the sample.

    • Gather rice that has fallen on the ground.

  • 12.

    During the Olympics, several events can take place at the same time. Describe a way to find a random sample of athletes who have an event at noon using the cluster random sample method.

    Answers:

    • Randomly choose a country and use those athletes as the sample.

    • Randomly choose one event and use all of those athletes as the sample.

    • Randomly choose a few athletes from each event as the sample.

    • Randomly choose a time of day and use one event as the sample.

  • 13.

    The members of a football team all have a unique jersey number. There are 5 different positions on the team, with 8 players in each position. Patrick wants to gather a sample of players on this team. Determine the cluster random sample that Patrick should use.

    Answers:

    • Randomize the jersey numbers to make a list, then use every 8th name on the list.

    • Randomize the jersey numbers to make a list, then use the first 8 names on that list.

    • Look at a sample of all 8 players in one randomly chosen position.

    • Look at a few players from each of the 5 positions.

  • 14.

    At a bingo game, 6 players are sitting at 50 different tables. Hannah wants to collect a sample of 6 players. Which of the following is a way for her to collect a sample of 6 using the cluster random sampling method?

    Answers:

    • Randomly choose one table and use all 6 at that table as the sample.

    • Randomly choose three tables and use 2 people from each table.

    • Put all of the players names in a bowl and pull out 6 names.

    • Select one person from each of the 6 tables closest to the door.

  • 15.

    A trivia game has 9 different categories and 4 questions in each category. Amy is playing and wants to select a sample of questions. In order to collect a cluster random sample, what should she do?

    Answers:

    • Randomly choose one category and look at all 4 of those questions.

    • Randomly choose one category and select one question from that category.

    • Randomly choose one question to start with, and select every 3rd question after that.

    • Randomly choose two questions from each of the categories.

  • 16.

    Mac loves movies so he subscribes to several different movie channels. For him to take a sample of movies and review their lengths, which of the following is the best cluster random sampling method?

    Answers:

    • Choose a few movies from each of the movie channels.

    • Choose one of the movie channels and randomly select the movie that is currently on.

    • Choose one of the movie channels and review the lengths of all movies on that channel.

    • Choose a random selection of movies from a schedule of all movies.

  • 17.

    There are 10 waitresses working at a diner, and the manager wants to collect a sample of orders. Using a cluster random sampling method, describe the steps the manager takes to find his sample.

    Answers:

    • Randomly choose one waitress and look at all of her orders.

    • Gather all of the orders and look at every 7th one.

    • Look at all of the orders the chefs are working on right now.

    • Randomly choose 6 orders from each of the waitresses.

  • 18.

    A group of people are separated into groups of red, black, and green. Martin wants to collect data from these people using a cluster random sample. How can this be done?

    Answers:

    • Spin a three color wheel, and look at all of the people in the group that matches the color on the wheel.

    • Spin a three color wheel several times, and select one person from each color on the wheel.

    • Line the people up and select every 12th person.

    • Assign each person a number, then draw numbers out of a bowl.

  • 19.

    A car dealership sells 8 different colored cars (labeled 1 through 8) with a variety of prices. To analyze the prices, figure out which option gives a cluster random sample.

    Answers:

    • Pick one car to start with, then roll an 8 sided die to find how many other cars to select.

    • Roll an 8 sided die, and look at all cars that match that number.

    • Roll an 8 sided die, and select that number of cars from each color.

    • Pick one car to start with, then roll an 8 sided die to indicate the location of the next car.

  • 20.

    A grocery store has 6 different brands of an oat cereal. Mama wants to do a taste test of a box of oats. When designing the experiment, she uses a cluster random sampling method. Select the best description of what she should do for this experiment.

    Answers:

    • None of the above describes a cluster sampling method.

    • Look at the shelf, select the first brand, then every other brand.

    • Take a randomly chosen amount from each of the six brands.

    • Randomly choose one brand and taste that box of cereal.

  • 21.

    Anna's large family gathered for her birthday. All different members brought her a gift. This included multiple aunts, uncles, cousins and siblings. She doesn't want to open every present, just a representative few. Determine how she can do this with a cluster random sample.

    Answers:

    • Open the gifts from the people that know her the best.

    • Randomly choose the type of family member and open all of their gifts.

    • Line up the gifts and open the first one. After that, open every 4th present.

    • Open a few gifts from each type of family member.

  • 22.

    An electronics manufacturer produces laptops, calculators, tablets and phones. For a quality control check, they decide a cluster random sample is the best method. Select the best description of their sample.

    Answers:

    • They randomly selected one type of product and tested all of that product.

    • They randomly selected one type of product and tested all of the newest versions of that product.

    • They randomly selected a certain number of items from each type of product.

    • They randomized a list of all ID numbers on all items and tested the items with the first 30 ID numbers.

  • 23.

    Each day, the Browns use a different amount of energy. They are able to track the exact amount each day. To gather one sample of data use in a day, they try the cluster sampling method. What steps can they take to do that?

    Answers:

    • Break down the usage into weeks. Randomly choose a day of the week. Look at the information for one hour each of those days.

    • Break down the usage into months. Randomly select 5 days from each month. Look at the information for those days.

    • Break down the usage into months. Randomly choose a number from 1 to 8. Look at the information from each date that has that number in it.

    • Break down the usage into weeks. Randomly select one week. Look at the information from all of the days in that week.

  • 24.

    Karen wants to estimate her overall GPA based on a sample of quiz scores. In 5 years, she has taken 20 quizzes each year. Rather than look at all of them, she decides to pick a sample of 20 using the cluster method. Select the best description of that method here.

    Answers:

    • Randomly choose one of the years and look at all 20 of those quizzes.

    • Reach into a folder and take out 20 quizzes at random.

    • Organize the quizzes by the date they were taken and take every other quiz until there are 20.

    • Randomly select 4 quizzes from each year and look at those 20.

  • 25.

    Georgia has a bookshelf with 7 shelves. She wants to take a sample of books. What is a way she could collect a clustered random sample?

    Answers:

    • Randomly select any book and take every 9th book after that.

    • Randomly select a sample based on an entire list of the books.

    • Randomly choose several books on each shelf.

    • Randomly choose a shelf and select all of the books on that shelf.

  • 26.

    Looking through an airplane catalog, Rusty is interested in the prices of items. Describe a way that Rusty could find a sample with the cluster method.

    Answers:

    • Select some items on the first page, then on every 10th page after that.

    • Flip to the middle and look at all of the items that are electronic.

    • Randomly select a few items from each page.

    • Flip to any page and look at the prices of all items on that page.

  • 27.

    Fans come from all over the country to see the Super Bowl. Pat is gathering information about the people at the game. Due to the size of the crowd, he decides to take a cluster random sample. What steps can he take to do that?

    Answers:

    • Randomly select a few people out of sections that are on the 2nd level.

    • Randomly select a few people out of each section of seats.

    • Randomly select one section of seats from the 2nd level and use all of those people as a sample.

    • Randomly select one person as they enter the stadium, then every 8th person after that.

  • 28.

    One of Zoe's chores is organizing laundry. She separates clothes into 5 different baskets. To check her progress, Zoe's mom takes a sample of clothes. Which of the following is a cluster random sample for this situation?

    Answers:

    • Randomly choose a family member and look at all of their clothes.

    • Randomly select a few items from each basket.

    • Look at the top 9 items in 3 of the baskets.

    • Look at all of the clothes in one basket.

  • 29.

    Housing prices are out of control! Zack wants to collect a sample of homes in 6 different cities using a cluster method to get the best representative sample. Which of the following is a good suggestion for him?

    Answers:

    • Make a randomized list of all homes, select the first one and then every 16th after that.

    • Randomly choose a few homes from each city.

    • Make a randomized list of all homes and analyze the first 100 on the list.

    • Randomly choose one city and analyze all of the homes in that city.

  • 30.

    Bob purchased 10 bags of M&Ms. He wants to gather a sample to investigate the colors. Describe how he could do that with the cluster random sampling method.

    Answers:

    • Randomly select one bag and look at all the candy in that bag.

    • Pour out all of the candy and select every 15th piece.

    • Pour out all of the candy and randomly pick enough candy to make a sample.

    • Randomly select a few candies from each of the 10 bags.

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