STAT 1301 Chapter 16 Chance Processes

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

Box Model: Used to draw analogy between chance process and drawing from a box

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?

General Principle #1: When Sampling WITH Replacement only the % of each type of ticket matters. these are “Identical” Boxes:

General Principle #2 If # of tickets is much larger than # draws, then - drawing WITHOUT replacement is similar to drawing WITH replacement

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 1Y10 1

The Point Is : simple box models can be used to illustrate sampling from a population

Draw 30 times from the following box max. average = min. average = max. sum = min. sum = 129