Confidence Intervals
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Confidence Intervals

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Questions and Answers

What does a point estimate indicate about a population parameter?

  • It provides the exact value of the population mean.
  • It confirms that prior data is irrelevant to the population mean.
  • It serves as an approximation of the population mean. (correct)
  • It reflects the uncertainty associated with the estimate.

    • Why are confidence intervals considered more informative than point estimates?

  • They provide a range where the true mean is likely to fall. (correct)
  • They require weighing all population members before calculations.
  • They eliminate any uncertainty regarding the population mean.
  • They are easier to calculate than point estimates.

    • What is the proper interpretation of a 95% confidence interval?

  • 95% of all possible confidence intervals will contain the population mean. (correct)
  • The sample mean must be exactly equal to the population mean.
  • There is a 95% chance the population mean is within the interval.
  • Confidence intervals are fixed and do not vary across samples.

    • How does prior information about sample means influence confidence intervals?

    <p>It can invalidate the confidence interval's relevance.</p> Signup and view all the answers

    What does the notation 72.85 < μ < 107.15 represent in a confidence interval?

    <p>It delineates a range for the population mean with 95% confidence.</p> Signup and view all the answers

    What is the consequence if a confidence interval does not account for prior studies indicating higher means?

    <p>The confidence interval could be misleading.</p> Signup and view all the answers

    Which of the following defines the purpose of a confidence interval?

    <p>To indicate a range where the population mean is likely found.</p> Signup and view all the answers

    What percentage of confidence intervals is expected to NOT contain the population mean at a 95% confidence level?

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

    What is a potential limitation of relying solely on confidence intervals?

    <p>They may not represent the population well if no prior data is considered.</p> Signup and view all the answers

    Which scenario suggests that a 95% confidence interval may not be reliable?

    <p>When previous studies indicate a mean above the upper interval limit.</p> Signup and view all the answers

    What is one key characteristic of the standard method of computing confidence intervals?

    <p>Each interval is contiguous.</p> Signup and view all the answers

    How is the standard error of the mean calculated if the population standard deviation is known?

    <p>It is the population standard deviation divided by the square root of the sample size.</p> Signup and view all the answers

    What conditions warrant the use of the t distribution instead of the normal distribution?

    <p>When the sample size is small and the population variance is estimated.</p> Signup and view all the answers

    What is the formula used to compute a 95% confidence interval for the mean?

    <p>Lower limit = M - Z.95 * σM; Upper limit = M + Z.95 * σM.</p> Signup and view all the answers

    What value of Z is typically used to determine the limits of a 95% confidence interval in a normal distribution?

    <p>1.96</p> Signup and view all the answers

    What does the term 'leptokurtic' describe in relation to the t distribution?

    <p>It has a shape that is more peaked than the normal distribution.</p> Signup and view all the answers

    When using the normal distribution with a sample size of 100 or above, what can be said about the t distribution?

    <p>It becomes similar to the standard normal distribution.</p> Signup and view all the answers

    What must be true in order to compute a confidence interval for a population mean?

    <p>Sample data must be normally distributed.</p> Signup and view all the answers

    If a researcher intends to calculate a 99% confidence interval, what is the corresponding value of Z used?

    <p>2.58</p> Signup and view all the answers

    What is the lower limit of the 95% confidence interval for the mean difference score?

    <p>14.17</p> Signup and view all the answers

    What is the critical value of t used in the computation for the 95% confidence interval for this data?

    <p>2.013</p> Signup and view all the answers

    What does the standard error of the mean represent in this context?

    <p>The measure of variability in the sample mean estimate.</p> Signup and view all the answers

    What is the upper limit of the 95% confidence interval for the mean difference score?

    <p>18.56</p> Signup and view all the answers

    If the sample mean (M) is 16.362, what does the term 'sM' refer to in the 95% confidence interval formula?

    <p>The estimated standard error of the mean.</p> Signup and view all the answers

    In the analysis of the Stroop data, how many subjects were recorded for the color-naming task?

    <p>47</p> Signup and view all the answers

    What is the calculated standard deviation of the mean time difference for the 47 subjects?

    <p>7.470</p> Signup and view all the answers

    How is the term 'interference effect' defined in the context of this analysis?

    <p>The effect of naming ink colors that conflict with the written word.</p> Signup and view all the answers

    What is the formula used to compute the confidence interval?

    <p>Lower limit = M - (tCL)(sM); Upper limit = M + (tCL)(sM)</p> Signup and view all the answers

    In the given example, what was the mean time difference for all subjects?

    <p>16.362 seconds</p> Signup and view all the answers

    Study Notes

    Point Estimates

    • A point estimate is a single value used to estimate a population parameter
    • It doesn't reveal the uncertainty associated with the estimate

    Confidence Intervals

    • A confidence interval provides more information than a point estimate
    • They capture the uncertainty associated with the estimate
    • A 95% confidence interval means that 95% of the time, the interval will contain the true population mean.

    Confidence Interval of the Mean: Population Standard Deviation Known

    • Confidence intervals can be computed for various parameters, not just the mean
    • Confidence intervals can be constructed by working backward from the population mean
    • Formula for the 95% confidence interval for the mean with a known population standard deviation:
      • Lower limit = M - Z.95σm
      • Upper limit = M + Z.95σm

    Confidence Interval of the Mean: Population Standard Deviation Unknown

    • Use the t-distribution when the variance is not known
    • Use the t-distribution when the sample size is small
    • Formula for the 95% confidence interval for the mean when the standard deviation is unknown:
      • Lower limit = M - (tCL)(sM)
      • Upper limit = M + (tCL)(sM)

    Stroop Effect Confidence Interval

    • The Stroop effect is the interference that occurs when naming the color of ink that words are written in, when the words are color names
    • The confidence interval of the mean for the Stroop effect difference score was computed using the t-distribution
    • Confidence interval for the difference between the interference and color-naming conditions:
      • Lower limit = 14.17
      • Upper limit = 18.56

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