Notes 54

1. Notes 54 Populations and Samples

2. Vocabulary Population-the entire group. Sample-part of the population that is studied. Random sample- members of the population are chosen at random. Convenience sample- based on members of the population that are readily available. Biased sample- does not fairly represent the population.

3. Helpful Hint A random sample is more likely to be representative of a population than a convenience sample is. 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.

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

5. 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. 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. 65% said the quarterback was the most valuable player. Check It Out: Example 1 Determine which sampling method will better represent the entire population. Justify your answer.

6. 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. 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.

8. 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.

9. 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 =

10. Additional Example 3 Continued Let x represent the number of actual students attending the band festival. 6 25 x 1500 = 6 • 1500 = 25 • x The cross products are equal. Multiply. 9000 = 25x 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.

11. 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.