7-3 Populations and Samples Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

7-3 Populations and Samples Warm Up Solve. n = – = 2. 8n = – n – 9 = – n9n9 n = –16 = n – (–30) n = –15 n = –46

7-3 Populations and Samples Problem of the Day Why are both products the same? 26  51 = 1,  34 = 1,  51 = (2  13)  (3  17); 39  34 = (3  13)  (2  17); They have the same factors: 2, 3, 13, and 17

7-3 Populations and Samples I can compare and analyze sampling methods.

7-3 Populations and Samples Vocabulary population sample random sample convenience sample biased sample

7-3 Populations and Samples In 2002, there were claims that Chronic Wasting Disease (CWD), or Mad Elk Disease, was spreading westward across North America. In order to verify claims such as these, the elk population had to be tested. When information is gathered about a group, such as the elk in North America, the entire group is called the population. Because testing each member of a large group can be difficult or impossible, researchers often study a part of the population, called a sample.

7-3 Populations and Samples For a random sample, members of the population are chosen at random. This gives every member of the population an equal chance of being chosen. A convenience sample is based on members of the population that are readily available, such as 30 elk in a wildlife preservation area. A random sample is more likely to be representative of a population than a convenience sample is. Helpful Hint

7-3 Populations and Samples Determine which sampling method will better represent the entire population. Justify your answer. Additional Example 1: Analyzing Sampling Methods 61% want blue uniforms Jon writes each band student’s name on a card. He questions those students whose name he draws. Results 84% want blue uniforms Sampling method Maria surveys only the band students she knows personally. Jon’s sample is a random sample, giving every band member equal chance to be surveyed, so it is the better method.

7-3 Populations and Samples Determine which sampling method will better represent the entire population. Justify your answer. Check It Out: Example 1 50% want practice early Anna-Maria questions the swimmers who are in her Biology class. Results 72% want practice early Sampling method Ferdinand surveys every other swimmer on the team. Ferdinand’s sample is a random sample, giving results that better represent the entire swimming team, so it is the better method.

7-3 Populations and Samples A biased sample does not fairly represent the population. A study of 50 elk belonging to a breeder could be biased because the breeder’s elk might be less likely to have Mad Elk Disease than elk in the wild.

7-3 Populations and Samples Determine whether each sample may be biased. Explain. Additional Example 2: Identifying Potentially Biased Samples A. The mayor surveys 100 supporters at a rally about the most important issues to be addressed by the city council. The sample is biased. The supporters may have different ideas than those not at the rally. B. The principal sends out questionnaires to all of the students to find out what kind of music students prefer at dances. The sample is random. The students all have a chance to respond.

7-3 Populations and Samples Determine whether each sample may be biased. Explain. Check It Out: Example 2 A. The owner of a record shop surveys only customers over the age of 18 who shop at his store. This is not random. Customers under the age of 18 do not have a chance of being chosen. B. The teacher writes the name of each student on a piece of paper and questions the students whose names are drawn. This sampling method is random. Each student has an equal chance of being chosen.

7-3 Populations and Samples A principal of a school with 1,500 students estimates that about 400 students will attend a band festival on Saturday. A random sample of 25 students showed that 6 of them will attend. Determine whether the principal’s estimate is likely to be accurate. Additional Example 3: Verifying Claims Based on Statistical Data Set up a proportion to predict the total number of students that will attend. Students attending sample # of Students sampled Students attending Student Population =

7-3 Populations and Samples Additional Example 3 Continued Let x represent the number of actual students attending the band festival x 1500 = = 25 xThe cross products are equal = 25x Multiply x 25 = Divide each side by 25 to isolate x. 360 = x The estimate is not accurate because the data shows that 360 students are likely to attend.

7-3 Populations and Samples The owner of a large chain restaurant with 1,200 employees estimates that about 250 employees will ask for winter vacation. A random sample of 40 employees showed that 8 of them will ask for the time off. Determine whether the owner’s estimate is likely to be accurate. Check It Out: Example 3 Set up a proportion to predict the total number of students that will attend. Employees surveyed for time off # of Employees surveyed Employees asking for time off Total # of Employees =

7-3 Populations and Samples Check It Out: Example 3 Continued Let x represent the number of actual employees asking for time off x 1200 = = 40 xThe cross products are equal = 40x Multiply x 40 = Divide each side by 40 to isolate x. 240 = x The estimate is accurate because the data shows that 240 employees will ask for time off.