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STAT 503 Quiz III

  1. When use Normal approximation
    • When n is large, coefficients hard to calculate
    • lots of possible values for Y
    • and p isn't close to 0 or 1
  2. Normal approximation equations
    • u = np
    • o = √np(1-p)
    • as long as np and n(1-p) are both at least 5
  3. Proportion of success in Normal approximation
    • p-hat = Y/n
    • µ = p
    • sd = √p(1-p)/n
  4. Continuity correction
    interval is y - .5 and y + .5
  5. Standard error
    • SE = s/√n
    • 'average' deviation when using the sample means as an estimate for the population mean
    • description of the mean as applies to population mean
  6. As n -> ∞
    • y-bar -> µ
    • s -> o
    • SE -> 0
  7. Confidence interval formulas
    • y-bar +/- ta/2(o/√n)
    • that area will contain (1-a)100% of all samples
  8. t-distribution
    • heavier tail
    • more to z curve with larger samples
    • had df
  9. t-table
    • gives t values in the table
    • z-values on bottom
    • alpha/2 is the given on top as the area to the right
  10. cofidence interval contains the population...
    x% of the time, and y-bar is always the middle value
  11. Validity of CI construction models
    • must be random samples
    • if n is small the pop. needs to be normal
    • if n is large the pop. can be t'whatever
  12. observational study v. controlled experiment
    observational - less certain of results
  13. Pool v. unpooled
    • pool when sd1 = sd2
    • usually use unpooled, easier
  14. unpooled SE
    Image Upload 2
  15. pooled SE
    Image Upload 4
  16. CI for µ1 - µ2
    Image Upload 6
  17. T-value Calc
    (Y-bar - µ) / (s/√n)
  18. if 95% CI contains Zero:
    "no significant difference" btw µ1 and µ2 at 5% level of significance
  19. If 95% CI does not contain zero
    it implies statistical difference btw µ1 and µ2 at 5% level of significance.
  20. Conditions for validity of hypothesis testing
    • same for CI
    • two independent random samples
    • normal or large samples
  21. H0
    • null hypothesis
    • default state (innocent)
  22. HA
    alternate hypothesis
  23. Hypothesis
    • either fail to reject H0
    • or
    • reject H0
  24. Errors with hypo decision
    • Type I error: rejected, when it was true
    • low upper limit = alpha
    • statements have = signs
    • Type II error: fail to reject when Ha is true
    • upper limit = beta
    • Power of a test Pr(reject H0 | Ha is true)
    • statements ≠ or < >
Author
MRK
ID
264574
Card Set
STAT 503 Quiz III
Description
Chapter V, VI
Updated

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