1. Stat 217 – Day 3
More terminology…

2. Previously
Observational unit: The entity of interest on which we collect data
Variable: The characteristics we are measuring on the observational units
Statistic: A number calculated from the observed data that summarizes the variable.
Probability: The long-run proportion of times an outcome occurs if the random process is repeated indefinitely under identical conditions.

3. Example
The probability of rolling two dice and getting a seven is
If I were to repeatedly roll dice forever, I would roll a 7 about 16.7% of the time in the long-run
Could list out all 36 possibilities and see how many of them correspond to a sum of 7
Could roll dice for a very long time and see how often get a seven
Could run a simulation of lots of dice rolls (making certain assumptions) and see how often a seven is “rolled”

4. Definition
A random process can be repeated a very large number of times under identical conditions. Outcomes are not known in advance but the probability of particular outcomes can be predicted.
Monty Hall
Rock-Paper-Scissors (e.g., one person)
We can often simulate a random process, but have to make assumptions…

5. Example
How could I simulate dice rolls?

6. Example
(a) As a professional Ro Sham Bo player you want to know if have a tendency to play rock too often.
Observational units: plays of the game
Binary Variable: rock or not rock
(b) To simulate plays of the game, need to know the probabilities for each option
(c) Is this probability larger than 1/3?

8. Example 3 Can dogs sniff out cancer?
Could ask one dog to try multiple times and see how often identifies the correct sample
Random process
Obs units = attempts
Variable = correct identification or not?
Parameter = the dog’s long-run proportion of correct identifications

9. Example 4
Suppose I wanted to estimate how much money Cal Poly students tend to spend on textbooks in a quarter, but I only have time to ask the students in this class how much they spent.
Statistic = average amount spent
This statistic is an estimate for the average amount spent by all Cal Poly students this quarter

10. Example 4
Suppose I wanted to estimate how much money Cal Poly students tend to spend on textbooks in a quarter, but I only have time to ask the students in this class how much they spent.
Statistic = average amount spent
This statistic is an estimate for the average amount spent by all Cal Poly students this quarter

11. Process vs. Population
Process = an ongoing set of potential observations under identical conditions
Population = entire collection of observational units we are interested in

12. Definition
A parameter is a numerical summary of a random process or a population
The statistic is our estimate of the parameter based on our set of data that we observed

13. Definition
A parameter is a numerical summary of a random process or a population
The statistic is our estimate of the parameter based on our set of data that we observed (the sample)

14. Definition
A parameter is a numerical summary of a random process or a population
The statistic is our estimate of the parameter based on our set of data that we observed (the sample)
n = “sample size”
Categorical data: proportions
Quantitative data: means

15. To Turn In With Partner, on a separate piece of paper, with 2 names
Identify the population or process of interest, the sample, the sample size, the variable, the parameter of interest, and the statistic.
For Thursday
Meet back in library!
Finish Lab 0
Submit one copy with both names
Read section P.2

16. The CA Lottery “Jackpot”
Winning anything in scratch off games: .20
A particular number coming up in Roulette: .026
A U.S. male living to be 100: .023
Picking all 5 numbers in Fantasy Five:
Being struck by lightning:
Picking all 6 numbers in SuperLotto:

17. The CA Lottery “Jackpot”
If you buy 50 tickets a week, you should win the jackpot once every 9,000 years
If you drive 10 miles to buy a Lotto ticket, you are four times more likely to get killed in a car crash on the way to buy the ticket than you are to win the jackpot
The odds are longer than flipping a coin and getting heads 24 times in a row