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Business 205

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Review Sampling Continuous Random Variables Central Limit Theorem Z-test

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Preview Type I error Type II error Power T-test

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Remember… What is the difference between a hypothesis and a null hypothesis? What is the goal of a test statistic? What is a critical region? What is a rejection region?

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Type I error You say the null hypothesis is false when it is in fact true. You agree with your hypothesis even though it isn’t true. Denoted by “α” (alpha) level How confident you are in your findings

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Type II error You say the null hypothesis is true when in fact it is false. You say your hypothesis is false but it is really true. Denoted by β (beta)

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Power Probability of the test leading us to reject the null hypothesis when it is false. Power = 1 - β

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Remember the Z? Used when the population standard deviation and standard error is known Forces a normal distribution What do you do if you don’t know the population’s standard error?!

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Welcome the T-test Used to test a hypothesis when the population standard error is not known. M = group mean, = population mean, SE = estimated standard error

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Estimated Standard Error When you don’t know the standard error of a population (which is the majority of the time….)

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T-test Example H1: The sample mean will be different from the population mean. Your sample has the following data: 10, 15, 2. You know the population mean is 8. You want to see if your hypothesis holds true at α =.05.

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T-test Example 10, 15, 2 Mean Sample = 9 Mean Population = 8 SS = 86 n = 3 Sample variance = 86/(3-1) = 43 Standard error = √(43/3) = 3.79 t = (9 – 8)/3.79 =.26

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T-test findings t =.26 t-critical = ± 4.303 4.303.26 Accept the null, reject the hypothesis. -4.303

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T-test Example 25, 10, 8 H1: The sample will be worse than the population. Mean Sample = Mean Population = 20 SS = n = Sample variance = Standard error = t =

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T-test findings H1: The sample will be worse than the population. t = t-critical = Conclusion?

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