Statistics Chapter 8 - Confidence Intervals

  1. What is the status of Image Upload 2 for z-based confidence intervals for a population mean?
    Image Upload 4 is known
  2. What is the status of Image Upload 6 for t-based confidence intervals for population mean?
    Image Upload 8 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 10
  11. What is the general form of the interval estimate for the population mean?
    Image Upload 12+/- Margin of Error
  12. What is the interval estimate of Image Upload 14 equation if Image Upload 16 is known?
    Image Upload 18
  13. What is Image Upload 20?
    The confidence coefficient
  14. What is Image Upload 22?
    The z-value that provides an area of Image Upload 24 in the upper tail of the standard normal prob distribution
  15. Assume:
    Population of all individual car mileages is ND
    Standard deviation (Image Upload 26) is 0.8
    A sample size (n) of 50
    Build a 95% interval estimate of Image Upload 28
    • We have 95% confidence that Image Upload 30 will be within +/- .22 mpg of the population mean
    • Image Upload 32
    • Image Upload 34 (from z-table)
    • Margin of error = (1.96)(.113) = .22
  16. If we have 95% confidence that Image Upload 36 will be within +/- .22 mpg of the population mean...
    Assume Image Upload 38 = 31.56
    What is the confidence interval?
    [31.56 +/- 0.22] = [31.34, 31.78]
  17. If Image Upload 40 = 0.10 (90% confidence) what is the confidence interval width?
    1.645
  18. If Image Upload 42 = 0.05 (95% confidence) what is the confidence interval width?
    1.96
  19. If Image Upload 44 = 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 46 when it is not known?
    • s
    • Sample standard deviation
  24. What is the t-score standard error equation?
    Image Upload 48
  25. What is the t-score equation?
    Image Upload 50
  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 52
  30. At what sample size is the z-distribution used INSTEAD of the t-distribution?
    Image Upload 54
  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 56 is not known)?
    Image Upload 58
  33. In a sample of 16 management consultants, the following statistics about hourly wages have been computed:
    Image Upload 60
    Image Upload 62
    Construct a  95% confidence interval (C.I.) estimate.
    Image Upload 64

    • Image Upload 66
    • Image Upload 68

    • Image Upload 70
    • Image Upload 72
Author
honestkyle
ID
211890
Card Set
Statistics Chapter 8 - Confidence Intervals
Description
Confidence Intervals
Updated