STAT 1301

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STAT 1301

• Chapter 16
• Chance Processes

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Chance Process

• outcome not predetermined
• involves chance
• Examples- amount of money won at roulette
• - Democrats in a random sample of voters
• - average GPA from a sample of 50 students
• Question -- How much variation is there in the
  outcomes?
• Box models help us understand this

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Box Model Used to draw analogy between chance
process and drawing from a box
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Key Considerations when Relating Sum of Draws
from a Box to Chance Process

• what tickets should be in the box?
• how many of each?
• number of draws?

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General Principle 1 When Sampling WITH
Replacement

• only the of each type of ticket matters.
• these are Identical Boxes

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General Principle 2

• If of tickets is much larger than draws,
  then
• - drawing WITHOUT replacement is similar to
  drawing WITH replacement

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Example 90,000 Adults in a City 60,000
- have headaches frequently 30,000 - do
not

• Simple Random Sample (SRS) of 50 adults
• Interested in in sample with headaches
• These are nearly equivalent chance processes
• taking a SRS sample (WITHOUT replacement) of 50
  people from the population and finding the in
  the sample with frequent headaches
• drawing 50 times WITH replacement from the box
  and finding the of tickets

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The Point Is

• simple box models can be used to illustrate
  sampling from a population

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• Draw 30 times from the following box
• max. average
• min. average
• max. sum
• min. sum

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