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Module 4 - Coggle Diagram

- - - - SD can come from population (SE(x bar) = sigma/sqrt(n))
        
        Sampling distribution is normal.
      - SD can come from sample (SE(x bar) = s/sqrt(n))
        
        Sampling distribution is described by t distribution.
    - - Unbiased and independent samples: satisfied by random sampling.
      - Nearly normal distribution: at least one of the sub-conditions is satisfied.
        
        a) Population is approximately normal
        
        or b) Data bell-shaped
        
        or c) n >= 30 -> Central Limit Theorem (CLT)
  - - - Random sample
      - Nearly normal: n = 45 >= 30
  - - - P( x >= 35) = 0.018
    - - SE = 5/sqrt(15) = 1.291
      - P (x >= 29.5) = 0.00005 ~ 0
      - Sampling distribution because it asks about an average from a sample.
      - The sampling distribution is approximately normal, because population is approximately normal.
      - Centered at 24.5 (u)
    - - 1) We got a very unusual sample and found an extreme outlier
      - 2) We accidentally used a biased sampling method.
      - 3) The parameter is not actually 24.5
  - - - single woman 0.3085
      - 10 women with SE = 6.325, P(x >= 170) = 0.0569
      - Averages are less variable than individuals, so we are more like to get individual measurements away from the parameter. Therefore, the single woman is more likely to weigh over 170 lbs.
    - - Since averages get less variable with larger sample sizes, averages from samples of size 30 are more likely to be near the parameter than an average from a sample of 20.
  - - - Using mean = 235 and SD = 14/sqrt(9) (to describe sampling distribution from which we draw our sample means), find P(x <= 230.728) = .18
- - - - As n increases, SE decreases. As n decreases, SE increases.
  - - - If we want to find probabilities associated with certain sample proportions, we can use the normal calculator.
- - - - 50(.45) = 22.5
      - 50(1-.45) = 27.5
      - Both at least 15
- - - - n = (pq/SE^2) = 514.75 -> 515
    - - Bell-shaped? Random
      - 515(.71) and 515(.29) >= 15
      - Mean = parameter = .71
      - SE = sqrt(.71(.29)/515) = .02
      - Find p(.7 <= x <= .75) = .669
- - - - Find p(180/230 <= x <= 190/230) = .5288
    - - Find p(x <= 175/230) = .009
- - - - Find P(.51 <= x <= .58) = .592