Statistics Chapter 8 - Confidence Intervals

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honestkyle
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211890
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Statistics Chapter 8 - Confidence Intervals
Updated:
2013-04-11 14:51:02
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confidence intervals probability stats
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Confidence Intervals
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  1. What is the status of  for z-based confidence intervals for a population mean?
     is known
  2. What is the status of  for t-based confidence intervals for population mean?
     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 
  11. What is the general form of the interval estimate for the population mean?
    +/- Margin of Error
  12. What is the interval estimate of  equation if  is known?
  13. What is ?
    The confidence coefficient
  14. What is ?
    The z-value that provides an area of  in the upper tail of the standard normal prob distribution
  15. Assume:
    Population of all individual car mileages is ND
    Standard deviation () is 0.8
    A sample size (n) of 50
    Build a 95% interval estimate of 
    • We have 95% confidence that  will be within +/- .22 mpg of the population mean
    •  (from z-table)
    • Margin of error = (1.96)(.113) = .22
  16. If we have 95% confidence that  will be within +/- .22 mpg of the population mean...
    Assume  = 31.56
    What is the confidence interval?
    [31.56 +/- 0.22] = [31.34, 31.78]
  17. If  = 0.10 (90% confidence) what is the confidence interval width?
    1.645
  18. If  = 0.05 (95% confidence) what is the confidence interval width?
    1.96
  19. If  = 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  when it is not known?
    • s
    • Sample standard deviation
  24. What is the t-score standard error equation?
  25. What is the t-score equation?
  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?
  30. At what sample size is the z-distribution used INSTEAD of the t-distribution?
  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 ( is not known)?
  33. In a sample of 16 management consultants, the following statistics about hourly wages have been computed:


    Construct a  95% confidence interval (C.I.) estimate.



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