Chapter 23

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Author:
damea134
ID:
306365
Filename:
Chapter 23
Updated:
2015-08-13 23:44:57
Tags:
Accuracy Averages
Folders:
Statistics
Description:
The Accuracy of Averages
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  1. Finding The SE of the Average 
    (of Box)
    SE for the average says how far the average of the dras is likely to be from the average of the box

    Formula = SE/#Draws

    Example:

    Draws = 25

    Average of box with numbers (1,2,3,4,5,6,7)

    • Ave box = 28(sum of Numbers)/7 = 4
    • SD = 2
    • EV = [(#draws) x (ave of box)] = 25 x 4 = 100
    • SE = Square Root (#draws) x SD] = 5 x 2 =10

    Box Averages

    • EV of box = Averages = 4
    • SE of box = SE for (Sum of Box)/(#draws) 10/25 = .4

    So the Average/EV of the (box) is 4 with a Chance error of .4
  2. Using the Normal Curve to estimate more
    Estimate that the average of the draws will be more than 4.2

    • #draws =100
    • ave = 4
    • EV = 4 x 100 = 400
    • SD = 2
    • SE = square root(100) x 2 (SD) = 20

    SE of Box = 20/100 = .2

    Ave= 4 give or take .2

    convert into SU 4 (Average) - 4.2/ 2 (SE) = 1 (SU)  

    • Solve for above 1 using normal scale =
    • Area between 1 = 68% - 100% = 32% /2 = 16%
  3. SE with no givin SD
    • Wants to know average incomes of 25000 families. 1000s families are sampled
    • #draws = 1000
    • total income= 62,396,714
    • Ave income = 62,396,714/1000 =62,400
    • SD = Unknown (SD is Found Using BootStrap Method [section, chp 21])

    SD (BootStrap Method) = 53,000

    SE can now be Caluclated

    • SE for sum = square-root (#draws) x SD
    • SE =  31.6 x 53000 = about 1,700,000

    now we need the SE for the Average (62,400)

    SE for Ave = SE/#draws = 1,700,000/1000 =1700

    Answer = 62,400 +- 1,700
  4. Which SE
    SE shows the likely size of the amount off. It is a give-or-take number

    SE for sum = Square Root (#draws) x SD

    SE for Averages = SE for Sum/#draws

    SE for count = SE for Sum, From box (1,0) 

    SE for Percent = (SE for count/#draws) x 100.
  5. Sampling Average
    Estimates the population average but is off by a little. The little is the SE

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