Sampling Methods Answers

A bicycle factory installs about 400 tires per day. Tires are installed Monday through Friday for 8 hours per day. The manager of the factory estimates the number of properly installed tires per week using the process below.In the first hour of work on Monday, 49 out of 50 tires were properly installed. So, there were about 8(49) = 392 properly installed tires on Monday.Considering 5 working days per week, 5(392) = 1,960 is the number of tires properly installed in one week.Which best explains the validity of the results?

A town hosts an Arbor Day celebration. Each of the 105 families attending gets to choose a sapling to take home as they leave. Michelle and Ari each design surveys in order to determine the average height of the saplings. Michelle samples the first 20 families leaving the celebration. Ari samples every fifth family leaving the celebration. Which best explains which student’s sample is likely to produce more valid results?

Students are voting on the color of T-shirts to wear on their field trip. There are 160 students–65 boys and 95 girls–going on the field trip. A random sample of students is chosen. Surveying the random sample produced a representative sample of the population. Which was most likely true of the representative sample?

Samantha and Luis are attempting to determine the average number of library books that seventh-grade students check out at one time. Samantha surveys every other seventh grade student leaving the library. She samples a total of 40 of the 200 seventh graders. Luis samples 30 of the 200 seventh grade students at random in the school cafeteria. Whose sample is the most random?

A group of tourists is determining the order in which to visit national landmarks in Washington, DC. The group contains 200 people. Of those people, 150 are adults, and 50 are children. A random sample of tourists in the group is chosen. Surveying the random sample produced a representative sample of the population. Which was most likely true of the representative sample?

Kari plans to sample 20 people of a population that contains 100 students. She wants to determine how many people wake up before 6 a.m. Which sample is the most random?

Charles wants to find out if the students in foreign language classes spend more time in class speaking in English or in the foreign language they are studying. Charles first gets class lists of all students taking foreign language classes. He then chooses 10 students from each different language class to survey. Which best explains why the sample he chose may not be a representative sample?

The chart below shows the distribution of the number of books in a library.Sahira chooses a random sample from the library and records the type of books in the chart below.Type of BookNumberFantasy10Literature25Children’s4Nonfiction11Which explains whether or not Sahira’s sample is representative?

Lorrie wants to determine the average amount of time that students at her school spend on the computer each day. There are 350 students in 15 classes. The number of boys and girls is approximately equal. Which is the most random sample?

Nathan and Jordan design surveys to determine the average amount of time bicyclists in a race spend training each week. Nathan surveys every fifth bicyclist crossing the finish line after a race. Jordan surveys the first five bicyclists to finish the race. Which best explains which sample is likely to be the most valid?