# Chapter 20

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1. Find the Expected Value
How to find expected value in a sample of 25000 people

• 10000 republicans
• 15000 democrats

Sample size = 100

Find the EV of republicans (not box)

To find the expected value you have to find the average of the box

• EV = (Number of draw x average of box)
• Solution:

ave of republicans = 10000/25000 =.04

EV = 100 (#draws) x .04 (Ave) = 40
2. Find the SD
Using SD ShortCut (289)
Formula:

Big# - Small# x [Square Root of (fraction of Big#) x (fraction of Small#)]

• Can only be used with two numbers
• 5,1,1,1

Example

(5-1) x

example 1,0

• 25000
• 10000 republicans
• 15000 democrats

1s, 0s

SD = (1-0) x [Square root of (10000/25000 x 15000/25000)] = 4.9
3. Finding the SE for Precentage
SE for Precentage = SE of sample/#Draws) x 100

How to find expected value in a sample of 25000 people

• 10000 republicans
• 15000 democrats
• Sample/draws = 100

SE for Number (Republicans)

• Find SD = 4.9 (or about 5)
• SE = 10 x .5 = 5
•
• Now use percentage formula

(.5/100) x 100% = 5%
4. Using Box Model
If there are more than 2 numbers use box model to Consisting of 1 & 0

example:

out of a 100000 samples

• 20% have shoes
• 50% are broke
• 10% are on crack

Draws =1000

Isolate the Variable it ask for into 1s & 0s

find expected value (EV) of people who have bad credit 40% or 40,000

find the SE  (need SD... this is where the box model shines)

40% bad credit and the 60% good credit

SD = Square Root of (.4 x .6) = .49

SE = Square Root of (1000draws) x (.49 SD)

SE = 15
5. Using the Normal Curve
out of a 100000 samples

• 20% have shoes
• 50% are broke
• 10% are on crack
• Draws =1000

Find percentage between 39% and 40% have bad credit

Need to convert into standard units

• EV = 40%
• SE = 15
• Convert to percent 15/1000 = 1.5%

• 39-40 = 1, 1/1.5 = +/- .67
• Now look a normal curve to find percentage