Statistics Chapter 8 - Confidence Intervals

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  1. What is the status of Image Upload for z-based confidence intervals for a population mean?
    Image Upload is known
  2. What is the status of Image Upload for t-based confidence intervals for population mean?
    Image Upload is unknown
  3. What two things does Statistical Inference involve?
    • Estimation
    • Hypothesis
  4. What do we use statistical inferences for?
    To make inferences about a parameter
  5. What are the two types of estimates of parameters?
    • Point estimate
    • Interval estimate
  6. What is a Interval Estimate?
    It's a point estimate with a +/- Margin of Error
  7. What is the purpose of an Interval Estimate?
    Provide info about how close the point estimate is to the parameter
  8. In an Interval Estimate, what does the Width depend on?
    How much confidence you want in your estimate
  9. What is Precision?
    Width of an interval
  10. What is Accuracy?
    Probability of the estimate being correct, defined as Image Upload
  11. What is the general form of the interval estimate for the population mean?
    Image Upload+/- Margin of Error
  12. What is the interval estimate of Image Upload equation if Image Upload is known?
    Image Upload
  13. What is Image Upload?
    The confidence coefficient
  14. What is Image Upload?
    The z-value that provides an area of Image Upload in the upper tail of the standard normal prob distribution
  15. Assume:
    Population of all individual car mileages is ND
    Standard deviation (Image Upload) is 0.8
    A sample size (n) of 50
    Build a 95% interval estimate of Image Upload
    • We have 95% confidence that Image Upload will be within +/- .22 mpg of the population mean
    • Image Upload
    • Image Upload (from z-table)
    • Margin of error = (1.96)(.113) = .22
  16. If we have 95% confidence that Image Upload will be within +/- .22 mpg of the population mean...
    Assume Image Upload = 31.56
    What is the confidence interval?
    [31.56 +/- 0.22] = [31.34, 31.78]
  17. If Image Upload = 0.10 (90% confidence) what is the confidence interval width?
    1.645
  18. If Image Upload = 0.05 (95% confidence) what is the confidence interval width?
    1.96
  19. If Image Upload = 0.01 (99% confidence) what is the confidence interval width?
    2.576
  20. What probability of values is between z-scores of -1.645 and +1.645?
    0.9000
  21. What probability of values is between z-scores of -1.96 and +1.96?
    0.9500
  22. What probability of values is between z-scores of -2.576 and +2.576?
    0.9900
  23. What is used instead of Image Upload when it is not known?
    • s
    • Sample standard deviation
  24. What is the t-score standard error equation?
    Image Upload
  25. What is the t-score equation?
    Image Upload
  26. What are the differences between the t-distribution and the z-distribution?
    • t-distribution is more spread out than the standard normal (z-distribution)
    • t-distribution is defined by the # of degrees of freedom (df = n - 1)
  27. What happens to the degrees of freedom (df) as n (sample size) increases?
    df increases
  28. What happens to the t-curve as the degrees of freedom (df) increases?
    • t-curve narrows
    • Spread decreases
    • Eventually approaches the standard normal curve
  29. At what sample size does the t-curve become very similar to the z-curve?
    Image Upload
  30. At what sample size is the z-distribution used INSTEAD of the t-distribution?
    Image Upload
  31. What's the differences between the t-table and the z-table?
    • t-table shows values to the RIGHT of the t-score
    • t-table is based on df and not n
  32. What is the Confidence Interval equation for the t-distribution (Image Upload is not known)?
    Image Upload
  33. In a sample of 16 management consultants, the following statistics about hourly wages have been computed:
    Image Upload
    Image Upload
    Construct a  95% confidence interval (C.I.) estimate.
    Image Upload

    • Image Upload
    • Image Upload

    • Image Upload
    • Image Upload
Author:
honestkyle
ID:
211890
Card Set:
Statistics Chapter 8 - Confidence Intervals
Updated:
2013-04-11 18:51:02
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confidence intervals probability stats
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Confidence Intervals
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