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From Statistics to the Real World Avoiding Common Mistakes Rebecca Graber AP Statistics pd. 3

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Sampling Distribution Models Fiction : Sampling distribution is the same as the distribution of a sample If you increase the sample size, each sample will become more normal Reality: The sampling distribution is based on an infinite number of samples, not just one If you increase the sample size, each sample will look more like the actual population

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Confidence Intervals Are Not: Probabilities (p is definitely established, we just don’t know what it is) Distributions (all values are equally likely) Definite intervals (they are one of an infinite number of confidence intervals, derived from different samples)

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EX: Wrong: “There is a 97% probability there is an elephant in my room” Right: “I am 97% confident there is an elephant in my room”

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Hypothesis Testing Red flags (conceptual): –“I accept Ho” : this is not an option, you either reject or fail to reject –No mention of P-value: the P-value is the entire point of the test –No given alpha: you can’t accept or reject an Ho without some sort of threshold, it must be decided BEFORE you do the test –Failure to check conditions Red flags (numerical) –Number of predicted failures < 10 –Forgetting to multiply P by 2 for a two-tailed test –Using sample data for the SD –Having a c.i. that includes Ho

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Hypothesis Test Ex (errors in red) Situation: Five years ago, 40% of all living rooms in the U.S. had an elephant hidden under the couch. Recently, a researcher looked through 20 houses in one neighborhood, and found 10 elephants. Has the proportion changed? Test: Ho: p =.4 Ha: p .4 (Alpha?) Conditions: 20 < 10% of all houses in the U.S. 10 successes, 10 failures both > 10 Random, independent sample One proportion z-test: SD= (.5*.5/20)^½ =.112 P-value = P(z >.1/.112) =.19 I accept Ho, so I think p=.4 (p-value? Significance?)

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Errors and Power of a Test Type I errors are always more serious (T/F) Type II errors are always more serious (T/F) The power of a test refers to the ability to detect any kind of error (T/F) We want to maximize beta (T/F) When looking for a Type II error, our guess of the true p is Ha (T/F)

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Errors and Power of a Test Type I errors are always more serious (T/ F ) Type II errors are always more serious (T/ F ) The power of a test refers to the ability to detect any kind of error (T/ F ) We want to maximize beta (T/ F ) When looking for a Type II error, our guess of the true p is Ha (T/ F )

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Which is more serious? Situation 1: Conducting a test to see if there is an elephant in the room. If I think there is one, I will have to pay $3,000 for elephant removal services to come. If the elephant is not removed, it will leave a nasty imprint on my floor. Situation 2: Conducting the same test. If I think there is an elephant, I will pay $20 for it to be removed. If the elephant remains in my living room for a long period of time, it will eventually cause my house to cave in.

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