6 does increasing the size of a sample necessarily

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6. Does increasing the size of a sample necessarily make the sample representative of a population? Give an example to support your explanation. Use what you learned about populations and samples to complete Exercises 3 and 4 on page 444. Understand Quantities Can the size of a sample affect the validity of a conclusion about a population? Math Practice New Power Plant For 32% Against 62% Don’t know 6% New Power Plant For 70 Against 425 Don’t know 5
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442 Chapter 10 Probability and Statistics Lesson 10.6 Lesson Tutorials An unbiased sample is representative of a population. It is selected at random and is large enough to provide accurate data. A biased sample is not representative of a population. One or more parts of the population are favored over others. Key Vocabulary population, p. 440 sample, p. 440 unbiased sample, p. 442 biased sample, p. 442 EXAMPLE Identifying an Unbiased Sample 1 You want to estimate the number of students in a high school who ride the school bus. Which sample is unbiased? A 4 students in the hallway B all students in the marching band C 50 seniors at random D 100 students at random during lunch Choice A is not large enough to provide accurate data. Choice B is not selected at random. Choice C is not representative of the population because seniors are more likely to drive to school than other students. Choice D is representative of the population, selected at random, and large enough to provide accurate data. So, the correct answer is D . 1. WHAT IF? You want to estimate the number of seniors in a high school who ride the school bus. Which sample is unbiased? Explain. 2. You want to estimate the number of eighth-grade students in your school who consider it relaxing to listen to music. You randomly survey 15 members of the band. Your friend surveys every fifth student whose name appears on an alphabetical list of eighth graders. Which sample is unbiased? Explain. Exercises 5–7 The results of an unbiased sample are proportional to the results of the population. So, you can use unbiased samples to make predictions about the population. Biased samples are not representative of the population. So, you should not use them to make predictions about the population because the predictions may not be valid.
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Section 10.6 Samples and Populations 443 EXAMPLE Determining Whether Conclusions Are Valid 2 EXAMPLE Making Predictions 3 You want to know how the residents of your town feel about adding a new stop sign. Determine whether each conclusion is valid. a. You survey the 20 residents who live closest to the new sign. Fifteen support the sign, and five do not. So, you conclude that 75% of the residents of your town support the new sign. The sample is not representative of the population because residents who live close to the sign are more likely to support it.
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