Statistical Interval Estimation
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Questions and Answers

What is a point estimate in statistics?

  • An estimate calculated using confidence intervals
  • An exact value of the population parameter
  • An estimate of a population parameter based on sample data (correct)
  • The average of all values in a sample

    • What is the purpose of inferential statistics?

  • To obtain an exact value of the population parameter
  • To calculate confidence intervals
  • To make generalizations about an unknown population based on sample data (correct)
  • To average together several values in the classified section of the newspaper

    • What do confidence intervals represent in statistics?

  • The exact value of the population parameter
  • A range of values within which the population parameter is likely to lie (correct)
  • The point estimate of the population parameter
  • The average of the sample data

    • Why are point estimates most likely not the exact value of the population parameter?

    <p>Because they are affected by random variability in the sample data</p> Signup and view all the answers

    What is the main concept behind constructing confidence intervals?

    <p>To estimate a range within which the population parameter is likely to lie</p> Signup and view all the answers

    What distinguishes inferential statistics from descriptive statistics?

    <p>Inferential statistics makes inferences about populations, while descriptive statistics summarizes sample data</p> Signup and view all the answers

    What is the point estimate for the population mean?

    <p>The sample mean, x ˉ</p> Signup and view all the answers

    What is the point estimate for the population standard deviation?

    <p>The sample standard deviation, s</p> Signup and view all the answers

    What is used to estimate the population mean?

    <p>Sample mean, x ˉ</p> Signup and view all the answers

    Which theorem states that in approximately 95% of the samples, the sample mean will be within two standard deviations of the population mean?

    <p>Central Limit Theorem</p> Signup and view all the answers

    What does the empirical rule apply to?

    <p>Bell-shaped distributions</p> Signup and view all the answers

    Which value is used to calculate the standard deviation for the sample mean?

    <p>$rac{σ}{√n}$</p> Signup and view all the answers

    What does a 95% confidence interval imply?

    <p>It contains the true mean μ</p> Signup and view all the answers

    What is between 𝑥̅− 0 and 𝑥̅+0.2 in 95% of all the samples?

    <p>$μ$</p> Signup and view all the answers

    What happens for only 5% of all the samples?

    <p>$x ˉ$ is not within 0.2 units of $μ$</p> Signup and view all the answers

    $𝜎 √𝑛$ is equal to what for this example?

    <p>$1 √100$</p> Signup and view all the answers

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