PSCI 2702 Chapter 5
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Questions and Answers

What is a primary reason social scientists use samples instead of entire populations?

  • Samples provide more accurate results than whole populations.
  • It is cheaper and easier to test small groups.
  • Researchers prefer samples to maintain data confidentiality.
  • Populations are typically too large and logistically challenging to survey completely. (correct)

    • What does inferential statistics enable researchers to do?

  • Collect qualitative data exclusively.
  • Make predictions about population parameters based on sample data. (correct)
  • Conduct research without any samples.
  • Precisely measure all individuals in a population.

    • Which of the following applications of inferential statistics is focused on determining the validity of a given hypothesis?

  • Estimation procedures
  • Qualitative analysis
  • Hypothesis testing (correct)
  • Descriptive statistics

    • In what context is the concept of a sampling distribution particularly important?

    <p>When understanding how sample statistics relate to population parameters.</p> Signup and view all the answers

    What is one major hurdle in conducting social science research related to populations?

    <p>The vast size of populations making comprehensive data collection unrealistic.</p> Signup and view all the answers

    What two applications of inferential statistics are highlighted in the content?

    <p>Estimation procedures and hypothesis testing</p> Signup and view all the answers

    What is a characteristic feature of populations that makes them challenging to study?

    <p>They are typically very large and complex.</p> Signup and view all the answers

    Why do social scientists aim to have theories tested in various populations?

    <p>To gain confidence that theories are robust and applicable.</p> Signup and view all the answers

    What happens to the sample means as you continue taking samples from the population?

    <p>They will start to cluster around the true population mean.</p> Signup and view all the answers

    What can be expected from the sampling distribution of sample means?

    <p>It will peak around the true population mean.</p> Signup and view all the answers

    If a sample includes only younger residents, what would likely happen to the sample mean?

    <p>It will be much lower than the true population mean.</p> Signup and view all the answers

    What does EPSEM stand for in the context of sampling?

    <p>Equal Probability of Selection Method.</p> Signup and view all the answers

    Why are non-representative samples considered rare?

    <p>Because they are less likely to occur in practice.</p> Signup and view all the answers

    What is expected to happen to the frequency of sample means that are far from the true population mean?

    <p>The frequency will decline as we move away from the mean.</p> Signup and view all the answers

    What is one characteristic of each different sample drawn from the population?

    <p>They will be unique combinations of individuals.</p> Signup and view all the answers

    If the true mean age of the population is known to be 30, what will be true about the sample means?

    <p>They will predominantly be around 30.</p> Signup and view all the answers

    What percentage of samples are expected to fall within ±1 standard deviation of the mean in a normal sampling distribution when the sample size is large?

    <p>68%</p> Signup and view all the answers

    What does the standard error represent in the context of a sampling distribution?

    <p>The standard deviation of the population divided by the square root of n</p> Signup and view all the answers

    What does the mean of the sampling distribution equal when linking a sample to the population?

    <p>Population mean</p> Signup and view all the answers

    What is the standard deviation of the sampling distribution called when estimating parameters from a sample?

    <p>Standard error</p> Signup and view all the answers

    What does the Central Limit Theorem state about sample means?

    <p>They approach normality as sample size increases</p> Signup and view all the answers

    Why is it impractical to know the actual mean of the sampling distribution?

    <p>It requires drawing all possible samples from the population.</p> Signup and view all the answers

    Which of the following conditions is necessary for the first theorem regarding sampling distribution to hold?

    <p>The population must be normally distributed</p> Signup and view all the answers

    In the context of sampling distribution, what is typically the relationship between the population size and the sample size used?

    <p>The sample size is a fraction of the population size.</p> Signup and view all the answers

    How does the sample size affect the sampling distribution of sample means according to the Central Limit Theorem?

    <p>Larger samples decrease the dispersion of the distribution</p> Signup and view all the answers

    What is the main goal when using a carefully drawn probability sample?

    <p>To infer information about the population.</p> Signup and view all the answers

    What is the relationship between the mean of the sampling distribution and the population mean?

    <p>They are always equal regardless of sample size</p> Signup and view all the answers

    What defines the characteristics of the sampling distribution?

    <p>Theorems related to sampling distributions</p> Signup and view all the answers

    What happens when the population distribution is known to be skewed but the sample size is large?

    <p>The sampling distribution approaches normality</p> Signup and view all the answers

    Which formula correctly represents the standard deviation of the sampling distribution?

    <p>σ / √n</p> Signup and view all the answers

    Which of the following best describes a normal sampling distribution?

    <p>It approaches a normal distribution as sample size increases.</p> Signup and view all the answers

    What is often true about the values of population mean and standard deviation in typical research situations?

    <p>They can be estimated from sample statistics</p> Signup and view all the answers

    What does the Central Limit Theorem imply about the mean of the sampling distribution compared to the population mean?

    <p>They should be very close in value.</p> Signup and view all the answers

    Which formula correctly represents the standard deviation of the sampling distribution?

    <p>$σ_x = σ/√n$</p> Signup and view all the answers

    What is a likely reason for the sampling distribution not appearing normal?

    <p>Not enough samples were taken.</p> Signup and view all the answers

    Which sample size is suggested to better approximate the population characteristics?

    <p>A sample size of 100 or more is recommended.</p> Signup and view all the answers

    When calculating the standard deviation of the population, what is the relationship you should expect with the standard deviation of the sampling distribution?

    <p>They will be very close in value.</p> Signup and view all the answers

    What is a common issue that can arise from using a non-random sampling method?

    <p>Distribution bias and deviation from normality.</p> Signup and view all the answers

    In SPSS, what is one of the first steps when performing random sampling?

    <p>Opening the relevant data file.</p> Signup and view all the answers

    What should the approximate number of samples be for a clearer view of normal distribution?

    <p>100 to 200 samples or more.</p> Signup and view all the answers

    Study Notes

    Introduction to Inferential Statistics

    • Social science research aims to test theories and hypotheses across various populations.
    • Large populations pose a challenge due to the impracticality of testing every member.
    • Inferential statistics allow us to draw conclusions about a population based on a sample.
    • Two key applications of inferential statistics are estimation procedures and hypothesis testing.
    • Estimation procedures involve "guessing" the population parameter based on sample data.
    • Hypothesis testing assesses the validity of a hypothesis about the population using sample outcomes.
    • The foundation of these inferential statistics lies in understanding sampling and the sampling distribution.

    Sampling Distribution

    • The sampling distribution is the theoretical distribution of sample means that would be obtained if we took all possible samples of a given size from a population.
    • It is crucial in inferential statistics as it allows us to link sample data to the underlying population.
    • The concept of the sampling distribution relies on two key theorems:
      • The first theorem states that if the population is normally distributed, the sampling distribution of sample means will also be normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
      • The second theorem, known as the Central Limit Theorem, removes the constraint of normality in the population. It states that even if the population is not normally distributed, the sampling distribution of sample means will approach normality as the sample size grows larger.

    Linking Samples to Populations

    • The sampling distribution is crucial because it clarifies the relationship between sample data and population parameters.
    • The sampling distribution enables us to estimate population parameters based on sample statistics.
    • This process involves drawing a single sample and using the known characteristics of the sampling distribution to infer information about the population.

    Symbols and Terminology

    • μ: Population mean
    • μx : Mean of the sampling distribution
    • σ: Population standard deviation
    • σx : Standard deviation of the sampling distribution (also known as the standard error)
    • n : Sample size

    Practical Applications of Sampling and the Sampling Distribution

    • The demonstration and exercise use the 2018 CCHS (Canadian Community Health Survey) data as a real-world example.
    • The exercise involves estimating the average BMI (Body Mass Index) from a random sample drawn from the CCHS database using the SPSS (Statistical Package for the Social Sciences) software.

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    Description

    This quiz explores the key concepts of inferential statistics, including sampling distributions, estimation procedures, and hypothesis testing. Understand how these tools help researchers draw conclusions about populations based on sample data. Dive into the methods used to validate hypotheses and learn about the foundation of statistical sampling.

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