Lesson APR-9 Teaching Point: Students will determine a representative sample by studying examples of biased and unbiased samples. Homework APR-9: Impact, page 289 #10 and Representative Sample Worksheet Do Now: State Test Prep: Which expression below is equivalent to a. ( ) b. ( ) c. ( ) ? d. ( ) Vocabulary Representative Sample: a sample with an equivalent ratio to that of the population. Unbiased Sample: a sample that accurately represents the entire population Biased Sample: one or more parts of the population that favors one characteristic over another 1 Lesson APR-9 Notes Anyone conducting a survey using a sample will want a method that is practical to perform. That gives three important questions to ask when examining whether a particular survey method is a good one.  Is the sample large enough to give accurate results?  Is the sample representative of the population?  Is the survey method practical? There are two types of Unbiased Samples:  Simple Random Sample: Each item or person in the population is as likely to be chosen as any other. For example, if each student’s name is written on a piece of paper and the place in a bowl to be picked without looking.  Systematic Random Sample: the items or people are selected according to a specific time or item interval. For example, if every 20th person is chosen from an alphabetical list of students attending a school There are two different ways that a sample can be Biased:  Convenience Sample: members of a population that are easily accessed. For example, to represent all the students attending a school, the principal surveys the students in one math class.  Voluntary Response Sample: only those who want to participate in the sampling. For example, students at a school who wish to express their opinions complete an online survey Think and Discuss – Groups (Impact page 283) For a statistics project, Alison’s group wanted to predict which of the following after-school activities were the favorites of seventh graders in the four schools in their district:  playing sports  playing music  listening to music  watching TV  going to the mall  playing video games  reading  drawing or painting How would you recommend that Alison’s group collect a sample that would help them make an accurate prediction? Make a list of suggestions. 2 Lesson APR-9 Develop and Understand: A – Groups (Impact page 284) Alison’s group proposed five strategies for conducting its survey. Strategy 1: Ask all 600 seventh graders in the four schools. Strategy 2: Distribute questionnaires to the 130 seventh graders at the district band competition next week. Strategy 3: Get a list of all the seventh graders in the district. Call 5% at random from each school. Strategy 4: Survey every third seventh grader out of the 125 in our school as they enter their homerooms. Strategy 5: Survey the 12 seventh graders on one student’s bus. 1. Which strategy or strategies do you think would give the least representative data? The most representative data? 2. Which strategy would give the smallest sample size? The largest sample size? 3. Which strategy seems the least practical? The most practical? 4. Which strategy do you think is the best? Explain your reasoning. 3 Lesson APR-9 Develop and Understand: B – Groups (Impact, page 285) Alison’s group decided to survey every fourth student to enter each seventh grade homeroom in the school. The six homerooms have 28 students each. The survey results are displayed below in a bar graph: Hours Spent Favorite After-School Activities 14 12 10 8 6 4 2 0 Playing Watching Playing Sports TV video games Going to Listening Reading the mall to music Playing music Drawing or painting Activity 1. How large is the sample of the students surveyed? 2. How many students in the sample prefer playing sports after school? 3. Based on the sample, predict how many in a district of 600 seventh graders would prefer reading? 4. Suppose you could choose one seventh grader from the 600 in Alison’s school district at random. What is the probability that he or she prefers playing video games? Explain how you found your answer. 5. If Alison was predicting the favorite leisure activities of all students in the district, from kindergarten to twelfth grade, would sampling only seventh graders give an accurate picture of the population? Explain. 4 Lesson APR-9 Independent Practice Determine whether each conclusion is valid. Justify your answer. 1. To evaluate the quality of their product, a manufacturer of cell phones checks every 50th phone off the assembly line. Out of 200 phones tested, 4 are defective. The manager concludes that about 2% of the cell phones produced will be defective. 2. To determine whether the students will attend an arts festival at the school, Oliver surveys his friend in the art club. All of Oliver’s friends plan to attend. So, Oliver assumes that all the students at his school will also attend. 3. A random sample of people at a mall shows that 22 prefer to take a family trip by car, 18 prefer to travel by plane, and 4 prefer to travel by bus. Is the sample method valid? If so, how many people out of 500 would you expect to say they prefer to travel by plane? Preferred Ways to Travel Bus 9% Car 50% Plane 41% 5