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Fundamentals of Statistics

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  • What is the definition of statistics?

    Statistics is the science of collecting, organizing, analyzing, and interpreting data to make decisions.

  • What are data in statistics?

    Data consist of information coming from observations, counts, measurements, or responses.

  • What is a population in statistics?

    A population is the collection of all outcomes, responses, measurements, or counts that are of interest in a study.

  • What is a sample in statistics?

    A sample is a subset or part of a population used to gain information about the population.

  • Why is random sampling important?

    Random sampling ensures the sample is representative of the population, allowing valid conclusions about the population.

  • What is a parameter?

    A parameter is a numerical description of a population characteristic.

  • What is a statistic?

    A statistic is a numerical description of a sample characteristic.

  • How do parameters and statistics differ in variability?

    A parameter is constant for a population, while a statistic can vary from sample to sample.

  • What is descriptive statistics?

    Descriptive statistics involves organizing, summarizing, and displaying data.

  • What is inferential statistics?

    Inferential statistics uses sample data to draw conclusions about a population.

  • Give an example of descriptive statistics in a study.

    Reporting that 18% of adults from households earning less than \$30,000 do not use the Internet is an example of descriptive statistics.

  • Give an example of inferential statistics in a study.

    Concluding that lower-income households have less Internet access based on a sample is an example of inferential statistics.

  • What is a census?

    A census is data collected from every member of a population.

  • Why is a census often impractical?

    Because populations are usually large, collecting data from every member is often impractical or impossible.

  • What is the mnemonic to remember parameter vs. statistic?

    Match the first letters: Population Parameter and Sample Statistic.

  • What is the importance of the U.S. Census?

    The census data determine congressional seats and distribution of public funds.

  • What is the cost trend of the U.S. Census over time?

    The cost has escalated from about \$91.5 million in 1950 to \$15.6 billion in 2020.

  • What is the difference between a population parameter and a sample statistic in practice?

    A population parameter describes the entire population, while a sample statistic describes only the sample and may vary.

  • What is an example of a population parameter?

    The average SAT math score of an entire freshman class is a population parameter.

  • What is an example of a sample statistic?

    The average leisure time from a survey of 9400 individuals is a sample statistic.

  • What are the two major branches of statistics?

    Descriptive statistics and inferential statistics.

  • What role does probability play in statistics?

    Probability is a basic tool used in inferential statistics to draw conclusions about populations from samples.

  • What is the goal of inferential statistics?

    To use sample data to make generalizations or predictions about a population.

  • What is the goal of descriptive statistics?

    To summarize and describe the main features of a data set.

  • Why must sample data be collected using appropriate methods?

    Inappropriate methods can lead to biased samples that do not represent the population, invalidating conclusions.

  • What is an example of a sample in a survey about stress at work?

    The 751 employees surveyed out of all U.S. employees represent the sample.

  • What is the population in a survey of teens about mental health?

    All teens in the United States are the population.