Warm Up Problem of the Day Lesson Presentation Lesson Quizzes 1

Warm Up Solve. 2 5 n 9 n = 111 3 5 1. 12 = 2. 8n = –0.5 n = –0.0625 2 5 n 9 n = 111 3 5 1. 12 = 2. 8n = –0.5 n = –0.0625 3. n – 9 = –14 n = –15 4. –16 = n – (–30) n = –46 2

Why are both products the same? 26  51 = 1,326 39  34 = 1,326 Problem of the Day Why are both products the same? 26  51 = 1,326 39  34 = 1,326 26  51 = (2  13)  (3  17); 39  34 = (3  13)  (2  17); They have the same factors: 2, 3, 13, and 17 3

Sunshine State Standards MA.7.S.6.1 Evaluate the reasonableness of a sample to determine the appropriateness of generalizations made about the population.

Vocabulary population sample random sample convenience sample biased sample 5

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. 6

For a random sample, members of the population are chosen at random 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

Additional Example 1: Analyzing Sampling Methods Determine which sampling method will better represent the entire population. Justify your answer. 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. 8

65% said the quarterback was Check It Out: Example 1 Determine which sampling method will better represent the entire population. Justify your answer. 65% said the quarterback was the most valuable player. Chad puts all of his team members’ names in a hat and draws the names of 10 players at random. He then asks each of those players to name the team’s most valuable player. Results 87% said the quarterback was the most valuable player. Sampling method Pedro asks each member of the football team’s offense to name the team’s most valuable player. 9

Check It Out: Example 1 Continued Chad’s method produces results that better represent the entire football team because his sample includes members of both the offense and the defense. 10

A biased sample does not fairly represent the population 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. 11

Additional Example 2: Identifying Potentially Biased Samples Determine whether each sample may be biased. Explain. 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 chooses student names at random and asks them what kind of music they prefer at dances. The sample is not biased. It is random because every student has a chance to respond. 12

Determine whether the sample may be biased. Explain. Check It Out: Example 2 Determine whether the sample may be biased. Explain. 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. 13

Additional Example 3: Verifying Claims Based on Statistical Data A principal of a school with 1,500 students estimates that about 350 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. Set up a proportion to predict the total number of students that will attend. Students attending sample # of Students sampled Students attending Student Population = 14

Additional Example 3 Continued 6 25 x 1500 Let x represent the number of actual students attending the band festival. = 6 • 1500 = 25 • x The cross products are equal. 9000 = 25x Multiply. 9000 25 25x 25 = Divide each side by 25 to isolate x. 360 = x Based on the sample, you can predict that 360 students will attend the band festival. The principal’s estimate is likely to be accurate. 15

Check It Out: Example 3 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. 16

Check It Out: Example 3 Continued 8 40 x 1200 = ; 40x = 9600 ; X = 240 The estimate is likely to be accurate because you can use the data to predict that 240 employees will ask for time off. 17

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 18

1. Determine which sample better represents the entire population. b Lesson Quiz: Part I 1. Determine which sample better represents the entire population. b a. A TV ratings service is surveying residents of Orlando who bought TVs in the last month about their favorite TV show. b. A TV ratings service called residents of Orlando randomly selected from the phone directory to conduct a survey about their favorite show. 19

2. Determine whether each sample may be biased. Explain. Lesson Quiz: Part II 2. Determine whether each sample may be biased. Explain. a. A convenience store surveys customers one morning to determine what products they may like the store to stock. b. Each student’s name is written on a slip of paper and placed in a box. One slip of paper is selected to determine the student to be the homeroom representative. Biased; at other times of the day, customers may have different preferences. Not biased; the sample is random. 20

Lesson Quiz: Part III 3. A local middle school has 2500 students. Morgan interviewed 75 of the students about their library habits. She found that 45 of the students checked out a book weekly. Predict the number of students likely to check out books weekly. 1500 students 21

Lesson Quiz for Student Response Systems 1. Determine which sample better represents the entire population. A. 100 people exiting a football stadium are surveyed to find out the favorite game of the city residents. B. 200 people of the city are randomly selected from the phone directory and surveyed to find out the favorite game of the city residents. C. 150 members of a golf club are surveyed to find out the favorite game of the city residents. 22

Lesson Quiz for Student Response Systems 2. Determine whether the sample may be biased. Explain. Smith surveys 35 people in the purchase department of his company to determine the favorite hobbies of the employees of the company. A. Biased; the other employees may have other preferences. B. Not biased; the sample is random. C. Biased; the sample is random. 23

Lesson Quiz for Student Response Systems 3. A machine produces 225,000 insulating washers for electrical devices per day. In a random sample of 200 washers, there were 4 defectives. Predict the number of defective washers produced by the machine per day. A. 2,250 B. 4,500 C. 9,000 D. 22,500 24