Chapter 23

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

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%

• 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

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.

Estimates the population average but is off by a little. The little is the SE