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Chapter 8: Problem 2

Student Archaeologists. An archaeological dig turns up large numbers of pottery shards, broken stone implements, and other artifacts. Students working on the project classify each artifact and assign it a number. The counts in different categories are important for understanding the site, so the project director chooses \(2 \%\) of the artifacts at random and checks the students' work. What are the population and the sample here?

Short Answer

Expert verified
Population: all artifacts found; Sample: 2% of artifacts checked.

Step by step solution

01

Define the Population

The population in this scenario includes all the artifacts that were discovered during the archaeological dig. This encompasses every pottery shard, broken stone implement, and any other artifacts uncovered at the site.
02

Define the Sample

The sample consists of the 2% of artifacts that the project director randomly selects to check the students' classification and numbers. This is a subset of the population.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Population
When we talk about the population in statistics, we are referring to the complete set of items or group of individuals that are being studied. In the context of the archaeological dig mentioned in the original exercise, the population includes every single artifact that was unearthed at the site. This means that if there are 10,000 pottery shards, broken stone implements, and other artifacts in total, all these items form the entire population.

Understanding the concept of a population is crucial because it forms the base from which we draw conclusions. To gauge the characteristics of a population, often measurements or observations are made. However, measuring an entire population is usually impractical due to time and resource constraints, hence the need for samples. The goal is to gain insights about the entire population by studying a representative portion of it.
Sample
A sample is essentially a smaller group selected from within the larger population. In the exercise, the 2% of artifacts randomly chosen by the project director serve as the sample. This sample is critical in statistics because it allows researchers to make inferences about the population's characteristics without examining every individual artifact.

Sampling is beneficial as it reduces the amount of work needed to understand a dataset while still providing valuable insights. Proper sampling ensures that each member of the population has a chance of being included, leading to more reliable results.
  • It saves time and resources.
  • It helps in obtaining more refined and detailed data."
By studying just 2% of the artifacts, the project director can check and validate the accuracy of students' classifications efficiently.
Random Selection
Random selection is a foundational concept in statistics, which involves choosing samples from a population in such a way that each member has an equal chance of being selected. In our archaeological dig scenario, the director uses random selection to ensure unbiased sampling of artifacts. This method is crucial for minimizing selection bias and increasing the reliability of the conclusions drawn from the data.

Why is random selection so important?
  • It ensures that the sample accurately represents the population.
  • It increases the credibility and accuracy of statistical analyses.
Random selection facilitates objectivity in research and helps ensure that results derived from the sample can be generalized to the population reliably. By utilizing this method, researchers can feel confident that their findings are reflective of what they would observe if they were able to study the entire population.

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Most popular questions from this chapter

Off-Campus Housing. A university's housing and residence office wants to know how much students pay per month for rent in off-campus housing. The university does not have enough on-campus housing for students, and this information will be used in a brochure about student housing. They obtain a list of the 12,304 students who live in off-campus housing and have not yet graduated and mail a questionnaire to 200 students selected at random. Only 78 questionairres are returned. (a) What is the population in this study? Be careful: about what group do they want information? (b) What is the sample? Be careful: from what group do they actually obtain information? The important message in this problem is that the sample can redefine the population about which information is obtained.

Election polls. In response to the question, "If the 2016 presidential elections were being held today, would you vote for Hillary Clinton or Donald Trump?," the New York Times reported the result as \(43 \%\) for Hillary Clinton and \(39 \%\) for Donald J. Trump on July 7, 2016. This result was described as a "National Polling Average." Here are some details on how the average was computed. The New York Times polling averages use all polls currently listed in The Huffingtan Post's polling database. Polls canducted more recently and polls with a larger sample size are given greater weight in computing the averages, and polls with partisan sponsors are excluded. 36 (a) Why do you think they gave greater weight to polls with larger sample sizes? (b) Why should more recent polls be given greater weight? What population were they interested in on July 7, 2016 , and how does that population continue to change over the election period? (c) Why were polls with partisan sponsors excluded?

The Pew Research Centers Report entitled "How Americans value public libraries in their communities, " released December 11, 2013, asked a random sample of 6224 Americans aged 16 and over, "Have you used a Public Library website in the last 12 months?" In the entire sample, \(30 \%\) said Yes. But only \(17 \%\) of those in the sample over 65 years of age said Yes. Which of these two sample percents will be more accurate as an estimate of the truth about the population? (a) The result for those over 65 is more accurate because it is easier to estimate a proportion for a small group of people. (b) The result for the entire sample is more accurate because it comes from a larger sample. (c) Both are equally accurate because both come from the same sample.

How Accurate Is the Poll? A Pew Research Center survey on Teens, Social Media \& Technology at the beginning of 2015 included 1060 teens, of which 614 were white, non-Hispanic; 101 were black, non-Hispanic; 236 were Hispanic; and 109 were other races or ethnic groups. Each teen sampled was asked about technology usage, including access to mobile devices, social media usage, and video game playing. The margin of error (we will give more detail in later chapters) was reported as \(63.7 \%\) for the entire sample. When considering technology usage of only the Hispanic teens, the margin of error was reported as \(68.1 \% .4\) What do you think explains the fact that estimates for Hispanic teens were less precise than for the entire sample?

Retweeters. Twitter and Compete, a marketing services company, conducted a survey to investigate some of the characteristics of those who retweet (reposting of someone else's tweet). Among other findings, it was found that Twitter users who retweet are demographically similar to those who don't, use Twitter more often during the day, and are more likely to use Twitter on a mobile phone. Here is the methodology section contained with the survey results: The findings are based on data from surveys fielded in the Lnited States during 2D12. Twitter and Compete worked together to build a questionnaire that asked respondents about their propersity to use Twitter and other services as well as the when, where, how and why of their usage patterns. Compete iaterviewed 655 Internet users in the U.S. for this study. 30 (a) Explain in simple language why it is important to know how the sample was selected when drawing conclusions about a survey. (b) Do you feel the methodology section adequately explains how this sample was selected? Explain why or why not. If not, what information is lacking. and why is it important?
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