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Stat 217 – Day 3 More terminology…
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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.
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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”
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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…
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Example How could I simulate dice rolls?
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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?
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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
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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
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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
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Process vs. Population Process = an ongoing set of potential observations under identical conditions Population = entire collection of observational units we are interested in
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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
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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)
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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
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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
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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:
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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
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