Sampling Distributions Quiz
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Questions and Answers

Which of the following best defines a sampling distribution in statistics?

  • The probability distribution of a given random-sample-based statistic (correct)
  • The probability distribution of all the individual sample values
  • The probability distribution of a population
  • The probability distribution of a sample mean

    • What does the sampling distribution allow analytical considerations to be based on?

  • The probability distribution of a sample mean
  • The probability distribution of a population
  • The probability distribution of a statistic (correct)
  • The joint probability distribution of all the individual sample values

    • In statistics, what is the sampling distribution of a statistic?

  • The probability distribution of all the individual sample values
  • The probability distribution of a sample mean
  • The probability distribution of a population
  • The probability distribution of the values that the statistic takes on (correct)

    • When can the sampling distribution be found theoretically?

    <p>When an arbitrarily large number of samples, each involving multiple observations, are used</p> Signup and view all the answers

    Why are sampling distributions important in statistics?

    <p>They provide a major simplification en route to statistical inference</p> Signup and view all the answers

    Which of the following best describes the shape of the sampling distribution of the mean in Example 6.1.1?

    <p>Bell curve</p> Signup and view all the answers

    What is the probability of obtaining a sample mean of 154 in Example 6.1.1?

    <p>2/16</p> Signup and view all the answers

    What is the probability of obtaining a sample mean less than 158 in Example 6.1.1?

    <p>3/16</p> Signup and view all the answers

    What is the probability of obtaining a sample mean greater than or equal to 160 in Example 6.1.1?

    <p>5/16</p> Signup and view all the answers

    What does the probability distribution in Example 6.1.1 represent?

    <p>Probability of the sample mean</p> Signup and view all the answers

    Study Notes

    Sampling Distribution

    • A sampling distribution is a probability distribution of a statistic obtained through repeated sampling from a population.
    • The sampling distribution allows analytical considerations to be based on the behaviour of the statistic in repeated samples.

    Characteristics of Sampling Distribution

    • The sampling distribution of a statistic is a probability distribution of the possible values of the statistic.
    • Theoretically, the sampling distribution can be found using the probability distribution of the underlying population.

    Importance of Sampling Distributions

    • Sampling distributions are important in statistics because they allow us to make inferences about a population based on a sample.

    Shape of Sampling Distribution of the Mean

    • The shape of the sampling distribution of the mean is approximately normal, even if the underlying population is not normally distributed.

    Example 6.1.1

    • The probability distribution in Example 6.1.1 represents the sampling distribution of the sample mean.
    • The probability of obtaining a sample mean of 154 is a specific value that can be calculated from the sampling distribution.
    • The probability of obtaining a sample mean less than 158 can be calculated from the sampling distribution.
    • The probability of obtaining a sample mean greater than or equal to 160 can be calculated from the sampling distribution.

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    Quiz Team

    Description

    Test your knowledge of sampling distributions in statistics with this quiz. Explore the concept of probability distribution for random samples and learn about various statistics such as sample mean and sample variance.

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