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**Chapter 12: Statistics and Probability**

Lesson 12-1: Samples and Studies

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**Then/Now You displayed results from studies.**

Classify and analyze samples. Classify and analyze studies.

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Vocabulary A population consists of all of the members of a group of interest. A sample, otherwise known as a subset, is a part of the population used/selected to draw conclusion about the population.

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**Choosing the sample There are many different ways to choose a sample.**

Some ways are biased, while others are totally random.

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**Types of Samples Simple Random Sample Systematic Sample**

Self-selected sample Convenience Sample Stratified sample

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Simple Random Sample In a simple random sample, each member of the population has an equal chance of being selected as part of the sample. Simple random samples are often very close representations of a population.

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Systematic Sample In a systematic sample, members are selected according to a specified interval from a random starting point.

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Self-Selected Sample In a self-selected sample, members volunteer to be included in the sample.

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Convenience Sample In a convenience sample, members that are readily available or easy to reach are selected.

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Stratified Sample In a stratified sample, the population is first divided into similar, non-overlapping groups.

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Example 1 Classify a Random Sample A. MOVIES Every fifth person walking out of a movie theater is asked to name their favorite type of movie. Identify the sample, and suggest a population from which it is selected. Answer: Sample: every fifth person leaving the theater; population: all moviegoers

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Example 1 Classify a Random Sample B. MOVIES Every fifth person walking out of a movie theater is asked to name their favorite type of movie. Classify the sample as simple, systematic, self-selected, convenience, or stratified. Explain your reasoning. Answer: Systematic; members are selected according to a specified interval.

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**Some samples are better than others**

Sample data are often used to estimate a characteristic of a population. Therefore, a sample should be selected so that it is representative of the entire population. Also, the larger the sample size, or the more samples taken, the more closely it approximates the population.

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Bias A bias is an error (intentional or unintentional) that results in a misrepresentation of the population. If a sample favors one conclusion over another, the sample is biased and the data are invalid.

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Example 2 Biased and Unbiased Samples A. STUDENT COUNCIL The student council surveys the students in one classroom to decide the theme for the spring dance. Identify the sample as biased or unbiased. Explain your reasoning. Answer: The sample is biased because the participants are not randomly selected. The sample is selected in one classroom.

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Example 2 Biased and Unbiased Samples B. SCHOOL The Parent Association surveys the parents of every fifth student on the school roster to decide whether to hold a fundraiser. Identify the sample as biased or unbiased. Explain your reasoning. Answer: Unbiased; the parents are picked randomly, and all have an equal chance of being picked.

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**After a sample is selected, information can be collected using one of the following study types**

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**Picking the right type of study**

The type of study is influenced by the following: Cost Time Objective of the study

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Example 3 Classify Study Techniques A. RETAIL A retailer wants to evaluate their performance in customer service. They contact 1000 random customers asking if they would complete an evaluation form. Determine whether this situation describes a survey, an observational study, or an experiment. Explain your reasoning. Answer: Survey; the data are gathered from responses given by members of the sample.

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Example 3 Classify Study Techniques B. VITAMINS Researchers analyze the reactions of rats to a vitamin. Determine whether this situation describes a survey, an observational study, or an experiment. Explain your reasoning. Answer: Experiment; rats that did not get the vitamin are the control group and rats that got the vitamin are the experimental group.

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More Bias!!! Bias can occur in sampling, but it can also occur in the design of a study. Survey questions can easily create bias by: Being confusing Encouraging the members of the sample to answer a certain way Causing a strong reaction Addressing more than one issue at a time

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Example 4 Biased and Unbiased Survey Questions A. Identify each survey question as biased or unbiased. If biased, explain your reasoning. How often do you exercise? Answer: This question is unbiased. It does not encourage participants to answer a certain way, and it is clearly stated.

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Example 4 Biased and Unbiased Survey Questions B. Identify each survey question as biased or unbiased. If biased, explain your reasoning. Do you like basketball? If so, do you prefer watching high school, college, or professional? Answer: Biased; the question addresses more than one issue.

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Example 5 Biased and Unbiased Experimental Designs BASEBALL A baseball bat manufacturer wants to test a new grip on their bats. They select 75 high school baseball players to try out the bat with the new grips and 75 other players to try out the old grips. Identify the experiment as biased or unbiased. If biased, explain your reasoning. Answer: Biased; members of the control group and the experimental group are not randomly selected.

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