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 (D)</p>
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What is the main concept behind constructing confidence intervals?

<p>To estimate a range within which the population parameter is likely to lie (A)</p>
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What distinguishes inferential statistics from descriptive statistics?

<p>Inferential statistics makes inferences about populations, while descriptive statistics summarizes sample data (C)</p>
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What is the point estimate for the population mean?

<p>The sample mean, x ˉ (D)</p>
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What is the point estimate for the population standard deviation?

<p>The sample standard deviation, s (D)</p>
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What is used to estimate the population mean?

<p>Sample mean, x ˉ (B)</p>
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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 (A)</p>
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What does the empirical rule apply to?

<p>Bell-shaped distributions (B)</p>
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Which value is used to calculate the standard deviation for the sample mean?

<p>$rac{σ}{√n}$ (A)</p>
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What does a 95% confidence interval imply?

<p>It contains the true mean μ (C)</p>
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What is between 𝑥̅− 0 and 𝑥̅+0.2 in 95% of all the samples?

<p>$μ$ (D)</p>
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What happens for only 5% of all the samples?

<p>$x ˉ$ is not within 0.2 units of $μ$ (A)</p>
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$𝜎 √𝑛$ is equal to what for this example?

<p>$1 √100$ (A)</p>
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