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Lying Contest A Hypothesis Testing Demonstration from Introductory Statistics

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“Though I am not naturally honest, I am so sometimes by chance.” from A Winter’s Tale

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Cast of Characters Contestants: Billy Bob Jones Herbert Von Glockenspiel (names have been changed to protect their reputations) Mind Readers: MSE Teaching Staff Production Staff: Ringmaster, Igor, Madam X

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Mind Readers’ Instructions The Contestant will be shown a card and he/she will tell you whether it is Red or Black. On the scantron you will record you best estimate as to whether the contestant is being truthful or lying. After 16 cards, turn the scanton over and repeat for the second contestant. Do not discuss your answers.

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Scoring Instructions Exchange scantrons with someone nearby. The Ringmaster and Igor will reveal cards 5-16 and identify the contestant’s answers as truth or lie. Count each correct mind reading as one and put the total at the bottom of the scantron. Turn the scantron over and repeat for answers 55-66. Pass your scored scantrons to Igor.

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Alternative Hypothesis Some people are more talented liars than others. Using self-reported estimates, two people were chosen to represent the extremes of lying talent. These two representatives will be called Master Liar and Novice Liar. Until now only Madam X has known the identity of Master Liar and Novice Liar. Ringmaster will now open the sealed envelope and reveal their identities. The Alternative Hypothesis is that the Master Liar will be harder to read.

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Null Hypothesis There is no difference in lying talent. Everyone is equally able to fool or not fool mind readers. The self-reported lying talent estimates are meaningless.

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Data and Statistics n = number of Mind Readers = number of scantrons. This is called the “sample size”. x i = novice correct - master correct for scantron i. xbar = mean of the x i s = standard deviation of the x i. µ = mean of (novice - master) for the population. t = (xbar - µ 0 )/(s/√n) = xbar/ (s/√n) = “significance level” = 5% P-value = likelihood of resultant xbar or more extreme tstar = the t value that indicates statistical significance, i.e. the t value for which P-value =

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Restatement of Hypotheses High positive values of (Novice - Master) are indicative of a difference in lying talent. Alternative Hypothesis: µ > 0, i.e. the population is better able to read the Novice. Null Hypothesis: µ = 0, i.e. the population has no difference in reading the Novice and the Master. If t > tstar we REJECT the Null Hypothesis and say that we have statistically significant evidence that the Master is a better liar than the Novice. If t < tstar we do NOT REJECT the Null Hypothesis and say that we did not find statistically significant evidence that the Master is a better liar than the Novice.

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Experiment Design Notes This is a “matched-pairs” design because we used only the difference between Novice and Master score pairs, one for each Mind Reader. This eliminates many error sources, makes the analysis easier, and makes the test more powerful. This is a “double-blind” experiment because neither the Ringmaster nor the Mind Readers knew in advance which contestant was the Master and which was the Novice. The population that I have suggested here is Community College Teachers. This makes it reasonable to treat our sample as a Simple Random Sample of this population.

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Results Hopefully by now the data has been entered into the Excel worksheet and you can see for yourself the values for t and tstar. There is more that can be done with this data/experiment. Perhaps you can suggest some hypotheses to test? Thanks to all who helped--the Dean, the Mind Readers, Billy Bob Jones, Herbert Von Glockenspiel, Igor, and the mysterious Madam X.

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Section 10.4: Hypothesis Tests for a Population Mean.

Section 10.4: Hypothesis Tests for a Population Mean.

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