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Chapter 1: Problem 2

Explain the difference between a population and a sample.

Short Answer

Expert verified
A population includes all observations in a study, while a sample is a smaller group selected from the population for practical data collection.

Step by step solution

01

Define Population

A population refers to the entire set of individuals, items, or data that you are interested in studying. It includes all possible observations that fit the criteria you are examining. For example, if you are studying the height of adult men in a country, the population would include the heights of all adult men in that country.
02

Define Sample

A sample is a subset of the population that is selected for the actual study. It is a smaller group taken from the population, meant to represent it. For instance, instead of measuring the height of every adult man in the country, you could measure the height of a selected group of 1,000 adult men, which would be your sample.
03

Explain Why We Use Samples

Samples are used instead of entire populations because it is often impractical or impossible to collect data from the entire population. Collecting data from a sample is typically more feasible in terms of time, cost, and resources.
04

Discuss Accuracy and Representation

For a sample to be useful, it must be representative of the population. This means the sample should reflect the characteristics of the population as accurately as possible to make valid inferences about the population. If a sample is not representative, it may lead to biased or incorrect conclusions.

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Key Concepts

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

Population
In statistics, a population is the entire group of individuals or instances about whom we are interested in drawing conclusions. It includes every member that fits the criteria you are examining. For example, if you want to study the eating habits of teenagers in a city, the population will include all teenagers living in that city.
Examining an entire population provides comprehensive insights. However, it鈥檚 often impractical because populations can be large. This is where samples come into play.
Sample
A sample is a smaller, manageable version of the population. It鈥檚 a subset specifically chosen to represent the larger group. For instance, if the population is all teenagers in a city, a sample might be 200 teenagers picked randomly from different areas of that city.
Using samples allows researchers to draw conclusions about the population without needing to survey everyone.
This saves time, effort, and resources. But, for the sample to be useful, it must accurately reflect the population it's taken from.
Representative Sample
A representative sample is one that closely matches the characteristics of the population as a whole. It ensures that the conclusions drawn from the sample apply to the entire population. To achieve this, researchers need to consider several factors:
  • Age
  • Gender
  • Income Level
  • Education Level
If a sample isn鈥檛 representative, it can lead to biased results.
For example, if you only include teenagers from affluent neighborhoods, you might miss out on understanding the habits of those from lower-income areas.
Data Collection
Data collection is the process of gathering information from different sources to answer a research question. There are various methods for collecting data, such as:
  • Surveys and questionnaires
  • Interviews
  • Observations
  • Experiments
Choosing the right method depends on the research question and the nature of the data needed.
Effective data collection is crucial for ensuring the reliability and validity of the research. Inaccurate data collection can lead to flawed results and conclusions.

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Most popular questions from this chapter

The survey has bias. (a) Determine the type of bias. (b) Suggest a remedy. To determine the public's opinion of the police department, the police chief obtains a cluster sample of 15 census tracts within his jurisdiction and samples all households in the randomly selected tracts. Uniformed police officers go door to door to conduct the survey.

In Problems 11-22, identify the type of sampling used. A survey regarding download time on a certain website is administered on the Internet by a market research firm to anyone who would like to take it.

A research objective is presented. For each, identify the population and sample in the study. The Gallup Organization contacts 1028 teenagers who are 13 to 17 years of age and live in the United States and asks whether or not they had been prescribed medications for any mental disorders, such as depression or anxiety.

Contrast the differences between qualitative and quantitative variables.

Is there an association between daily coffee consumption and the occurrence of skin cancer? Researchers asked 93,676 women to disclose their coffeedrinking habits and also determined which of the women had nonmelanoma skin cancer. The researchers concluded that consumption of six or more cups of caffeinated coffee per day was associated with a reduction in nonmelanoma skin cancer. Source: European Journal of Cancer Prevention, \(16(5): 446-452,\) October 2007 (a) What type of observational study was this? Explain. (b) What is the response variable in the study? What is the explanatory variable? (c) In their report, the researchers stated that "After adjusting for various demographic and lifestyle variables, daily consumption of six or more cups was associated with a \(30 \%\) reduced prevalence of nonmelanoma skin cancer." Why was it imnortant to adiust for these yariables?
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