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**4-1 Samples and Surveys Warm Up Problem of the Day Lesson Presentation**

Pre-Algebra

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**4-1 Samples and Surveys Warm Up Evaluate. 1. t + 15 for t = –5**

Pre-Algebra 4-1 Samples and Surveys Warm Up Evaluate. 1. t + 15 for t = –5 2. n + (–13) for n = 7 Solve for x. = –21 4. 7x = –98 10 –6 x –3 x = 63 x = –14

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Targeted Instruction

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Problem of the Day Mr. Gray’s 29 students will be sitting in the gym to watch a play. There are two rows of five chairs, three rows of four chairs, and four rows of two chairs. Is there enough room for all the students to sit? yes

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**Learn to recognize biased samples and to identify sampling methods.**

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**Vocabulary population sample biased sample random sample**

systematic sample stratified sample

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**A fitness magazine printed a readers’ survey**

A fitness magazine printed a readers’ survey. Statements 1, 2, and 3 are interpretations. Which do you think the magazine would use? 1. The average American exercises 3 time a week. 2. The average reader of this magazine exercises 3 time a week. 3. The average reader who responded to the survey exercises 3 time a week.

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**A fitness magazine printed a readers’ survey**

A fitness magazine printed a readers’ survey. Statements 1, 2, and 3 are interpretations. Which do you think the magazine would use? The population is the entire group being studied. The sample is the part of the population being surveyed. 1. The average American exercises 3 time a week. 2. The average reader of this magazine exercises 3 time a week. 3. The average reader who responded to the survey exercises 3 time a week.

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For statement 1, the population is all Americans and the sample is readers of the fitness magazine who chose to respond. This is a biased sample because it is not a good representation of the population The population is the entire group being studied. The sample is the part of the population being surveyed. 1. The average American exercises 3 time a week. 2. The average reader of this magazine exercises 3 time a week. 3. The average reader who responded to the survey exercises 3 time a week.

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**Additional Example 1A: Identifying Biased Samples**

Identify the population and the sample. Give a reason why the sample could be biased. A. A record store manager asks customers who make a purchase how many hours of music they listen to each day. Population Sample Possible Bias Customers who make a purchase might be more interested in music than others in the store Music store customers Customers who make a purchase

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**Additional Example 1B: Identifying Biased Samples**

Identify the population and the sample. Give a reason why the sample could be biased. B. An eighth-grade student council member polls classmates about a new school mascot. Population Sample Possible Bias Students in the school Classmates She polls more eighth-graders than students in other grades.

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**Additional Example 1C: Identifying Biased Samples**

Identify the population and the sample. Give a reason why the sample could be biased. C. A television reporter asks people on downtown streets if they support a new city subway system. Population Sample Possible Bias People in the city People on downtown streets People working downtown might show more support than people who work elsewhere.

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**Population Sample Possible Bias**

Try This: Example 1A Identify the population and the sample. Give a reason why the sample could be biased. A. The first 5 people leaving a movie theater at a sneak preview were asked how they liked the movie. Population Sample Possible Bias People that really enjoy a movie are less likely to be of the first ones to leave. People that went to the movie The first five people that left

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**Population Sample Possible Bias**

Try This: Example 1B Identify the population and the sample. Give a reason why the sample could be biased. B. Eighth-grade students with a 3.0 GPA or higher were polled to determine how long students study each day. Population Sample Possible Bias Eighth grade students Students with 3.0 or higher GPA Students with lower grades are less likely to study as long.

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**Population Sample Possible Bias**

Try This: Example 1C Identify the population and the sample. Give a reason why the sample could be biased. C. People attending a baseball game were asked if they support the construction of a new stadium in the city. Population Sample Possible Bias People that attend a baseball game are more likely to support the construction of a new stadium. City residents People attending a game

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**Additional Example 2A: Identifying Sampling Methods**

Identify the sampling method used. A. In a county survey, Democratic Party members whose names begin with the letter D are chosen. systematic The rule is to survey members whose names begin with D.

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**Additional Example 2B: Identifying Sampling Methods**

Identify the sampling method used. B. A telephone company randomly chooses customers to survey about its service. random Customers are chosen by chance.

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**Additional Example 2C: Identifying Sampling Methods**

Identify the sampling method used. C. A high school randomly chooses three classes from each grade and then draws three random names from each class to poll about lunch menus. stratified The three classes are the random subgroups. Names are chosen randomly from within the classes.

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**Identify the sampling method used.**

Try This: Example 2A Identify the sampling method used. A. In a county survey, families with 3 or more children are chosen. systematic The rule is to survey families with 3 or more children.

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**Identify the sampling method used.**

Try This: Example 2B Identify the sampling method used. B. A retail home improvement store randomly selects customers to take a survey about their shopping experience. random Customers are chosen by chance.

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**Identify the sampling method used.**

Try This: Example 2C Identify the sampling method used. C. At a basketball game 5 sections are chosen at random and 20 people from each section are randomly polled. stratified The five sections are the random subgroups. 20 people are chosen randomly from within the sections.

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**Population Sample Possible Bias**

Lesson Quiz: Part 1 Identify the population and sample. Give a reason why the sample could be biased. 1. A high school principal asks the first three people who leave the school play whether they liked it. Population Sample Possible Bias People that went to the play The first 3 people leaving People that enjoy a play may not leave as early as someone who didn’t.

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Lesson Quiz: Part 2 Identify the sampling method used. 2. At a baseball game, 10 sections are chosen at random and 10 random people from each section are polled. 3. A telemarketer calls the people that have a last name beginning with H. stratified systematic

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