Calculating Mean and Standard Error with Confidence Intervals
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Questions and Answers

What does a narrow confidence interval indicate about the sample mean?

  • It is biased
  • It is imprecise
  • It is highly variable
  • It is fairly precise (correct)

    • In constructing a confidence interval, what are calculated to determine the range?

  • The mean and median
  • The standard deviation and variance
  • The mode and range
  • The lower and upper bounds (correct)

    • What percentage of the time would a 95% confidence interval fail to include the population parameters if the experiment were repeated multiple times?

  • 15%
  • 1%
  • 10%
  • 5% (correct)

    • What does the value of 'α' represent in the context of confidence intervals?

    <p>Confidence level</p> Signup and view all the answers

    In a two-tailed test for a confidence interval, what implication does having two alternatives hold?

    <p>It involves considering both sides of the distribution</p> Signup and view all the answers

    What calculation method is utilized to determine the lower and upper bounds in a confidence interval?

    <p>$t$-distribution</p> Signup and view all the answers

    What is the first step in calculating a 95% confidence interval for a mean?

    <p>Find the mean and its standard error</p> Signup and view all the answers

    In finding a 95% confidence interval for a mean, what does multiplying the standard error by 1.96 help to determine?

    <p>The margin of error for the estimate</p> Signup and view all the answers

    What is the purpose of calculating a confidence interval for a mean value in statistics?

    <p>To estimate how precise the mean estimate is</p> Signup and view all the answers

    What does a 95% confidence interval of 200.1 to 211.9 mean in relation to a population mean?

    <p>The population mean falls between 200.1 and 211.9 with 95% probability</p> Signup and view all the answers

    Which mathematical operation is used to determine the upper limit of a 95% confidence interval?

    <p>Addition</p> Signup and view all the answers

    If the standard error for a mean is 4, what is the margin of error when calculating a 95% confidence interval?

    <p>+7.84</p> Signup and view all the answers

    What action was taken regarding the null hypothesis when the value calculated for t (3.75) was not between ± 0.975?

    <p>Rejected the null hypothesis H0</p> Signup and view all the answers

    Which value is considered too unlikely or rare in the context of hypothesis testing?

    <p>Sample mean 𝒙 = 75.0kg</p> Signup and view all the answers

    What parameter helps in detecting a difference of a specified magnitude in hypothesis tests?

    <p>Statistical power</p> Signup and view all the answers

    What did setting the alpha level at a=0.05 determine in the hypothesis testing scenario mentioned?

    <p>Rarity cut points</p> Signup and view all the answers

    What was the consequence of deeming the observed outcome too unlikely or rare under the assumption of the null hypothesis being true?

    <p>Rejecting the null hypothesis H0</p> Signup and view all the answers

    In hypothesis testing, what measure can be easily obtained to determine the rarity of an observed outcome assuming the null hypothesis is true?

    <p>-2.26 as the critical value</p> Signup and view all the answers

    What does a 95% confidence interval for a percentage represent?

    <p>The range of values within which the percentage would be found at least 95% of the time.</p> Signup and view all the answers

    Why is the statement 'There is a 95% probability that the true effect is located within the confidence interval' incorrect?

    <p>The true effect is not a random variable; it is constant.</p> Signup and view all the answers

    How would you describe transforming the standard error into a 95% confidence interval?

    <p>It is straightforward.</p> Signup and view all the answers

    Which of the following best describes a 95% confidence interval?

    <p>It represents where the true effect lies 95% of the time.</p> Signup and view all the answers

    Why can't we assign a probability to whether the true effect is within a confidence interval?

    <p>The true effect is constant, not a random variable.</p> Signup and view all the answers

    What does a confidence interval represent?

    <p>The range of values consistent with the data from a study</p> Signup and view all the answers

    Why do epidemiologists often interpret confidence intervals as guides rather than strict ranges?

    <p>Because different formulas can sometimes give different results</p> Signup and view all the answers

    How is the precision of an estimate related to the width of a confidence interval?

    <p>As the interval narrows, the estimate becomes more precise</p> Signup and view all the answers

    What criterion is commonly used to determine the size of a confidence interval?

    <p>The width of the interval that includes the mean 95% of the time</p> Signup and view all the answers

    What is one reason why epidemiologists use a common-sense approach to interpreting confidence intervals?

    <p>Because different formulas can lead to varying results</p> Signup and view all the answers

    Which of the following is NOT a property or use of confidence intervals?

    <p>Representing an exact value from a study</p> Signup and view all the answers

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