Lesson Menu Main Idea and New Vocabulary Concept Summary: Unbiased Samples Concept Summary: Biased Samples Example 1:Determine Validity of Conclusions Example 2:Determine Validity of Conclusions Example 3:Use Sampling to Predict

Main Idea/Vocabulary Predict the actions of a larger group by using a sample. unbiased sample simple random sample stratified random sample systematic random sample biased sample convenience sample voluntary response sample

Key Concept

Key Concept 1A

Example 1 Determine Validity of Conclusions Determine whether the following conclusion is valid. Justify your answer. Every tenth student who walked into the cafeteria was surveyed to determine his or her favorite lunch. Out of 40 students, 19 students stated that they liked the burgers best. The cafeteria staff concluded that about 50% of the students like burgers best. Answer: The conclusion is valid. Since the population is the students who eat in the cafeteria, this is an unbiased, systematic random sample.

Example 1 CYP A.The conclusion is valid. Since the population is the customers who shop at the drugstore, this is an unbiased, systematic random sample. B.The conclusion is not valid because they should have surveyed people who weren’t in the drugstore. This is a biased, convenience sample. Determine whether the following conclusion is valid. Justify your answer. Every 5th drugstore customer was asked if they used the store brand toothpaste. Out of 85 people surveyed, 20 people indicated they did use the store brand toothpaste. The drugstore manager concluded that about 25% of the store’s customers used the store brand toothpaste.

Example 2 Determine whether each conclusion is valid. Justify your answer. Janet surveyed the student athletes on the girls’ field hockey team to determine which sports teenagers like best. Of these, 65% said that they like field hockey best. Janet concluded that over half of teenagers like field hockey best. Determine Validity of Conclusions Answer: The conclusion is not valid. The girls on the field hockey team probably like field hockey. This is a biased sample. The sample is a convenience sample since all of the people surveyed are in one specific location.

Example 2 CYP A.The conclusion is not valid because Dorothy surveyed people at a volunteer organization. This is a biased, voluntary response sample. B.The conclusion is not valid because Dorothy surveyed people at a specific location related to birds. This is a biased, convenience sample. Determine whether each conclusion is valid. Justify your answer. Dorothy surveyed the members of the local bird- watching organization to indicate their favorite animal. Of the people surveyed, 80% indicated that birds are their favorite animals. Dorothy concluded that most people like birds.

Example 3 Use Sampling to Predict BOOKS The student council is trying to decide what types of books to sell at its annual book fair to help raise money for the eighth grade trip. It surveyed 40 students at random. The books they prefer are in the table. If 220 books are to be sold at the book fair, how many should be mysteries?

Example 3 First, determine whether the sample method is valid. The sample is a simple random sample since customers were randomly selected. Thus, the sample method is valid. Use Sampling to Predict or 30% of the students prefer mysteries. So, find 30% of 220. Answer: About 66 of the books should be mysteries. 0.3 × 220 = 66

Example 3 CYP A.about 15 gallons B.about 11 gallons C.about 10 gallons D.about 6 gallons ICE CREAM An ice cream shop is trying to decide which flavors of ice cream to order. The employees surveyed 40 customers at random. The flavors the customers prefer are in the table. If the store is planning to order 30 gallons of ice cream, how many should be vanilla?