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Ch. 17 The Expected Value & Standard Error

Ch. 17 The Expected Value & Standard Error. Review box models Examples Pigs – assume 40% chance of getting a “trotter” 20 tosses Coin toss – 20 times Roll die – 10 times Roll die and count number of 5’s – 10 times. Expected Value (EV).

jessica-blanchard
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Ch. 17 The Expected Value & Standard Error

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  1. Ch. 17 The Expected Value & Standard Error • Review box models • Examples • Pigs – assume 40% chance of getting a “trotter” • 20 tosses • Coin toss – 20 times • Roll die – 10 times • Roll die and count number of 5’s – 10 times

  2. Expected Value (EV) • The expected value for a sum of draws made at random with replacement from a box equals (# of draws)x(average of box). • Pigs: EV=(20)(4/10)=8 • Coin toss: • 10 die rolls: • 10 die rolls and count # of 5’s:

  3. Standard Error (SE) • Sum = Expected Value + Chance Error • Standard error is how large the chance error is likely to be. • The sum of draws within 1 SE of EV is approximately 68% of the data. • The sum of draws within 2 SE of EV is approximately 95% of the data. • The sum of draws within 1 SE of EV is approximately 99.9% of the data.

  4. SE for sum = square root(# of draws)xSDbox • Example 1: Coin toss 20 times and let the sum be the number of heads. • Find the SE of the sum. • Find the average of the box • Find the SD of the box • Find the SE of the sum • Fill in the blanks: The number of heads in 20 coin tosses is likely to be ___ give or take ___ or so.

  5. Example 2: 10 die rolls • Find the average of the box • Find the SD of the box • Find the SE of the sum • The sum of 10 die rolls is likely to be ___ give or take ___ or so.

  6. Example 3: (A shortcut for boxes with only 2 kinds of tickets.) Roll a die 10 times and count the # of 5’s. • SD = • SE = • The number of 5’s in 10 die rolls is likely to be around ___ give or take ___.

  7. Using the normal table • Way to generalize a large number of draws with replacement. • Calculate the EV & SE for sum of draws • Repeat many times • Make a histogram of the sums

  8. Example 4: 100 draws with replacement from 1, 2, 3. Smallest sum = Largest sum = Average = EV = SD of box = SE of sum = We expect the sum of 100 draws to be ____ give or take ____.

  9. If we repeat this scenario many times, what percent of the time will the sum be above 220? (In other words, what is the probability of getting a sum greater than 220?)

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