9_t_Test_Single_Mean_Outline

9_t_Test_Single_Mean_Outline - 1 2 t Test for a Single...

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t Test for a Single Population Mean z test vs. t test –Known population standard deviation –Unknown population standard deviation t test • Degrees of freedom t distributions • Assumptions • Measures of effect size Example: Bills Fans’ IQs • We know that the national average for IQ scores is 100 with a standard deviation of 16. • We sample 5 people at a tailgate party at Ralph Wilson Stadium and test their IQs. • Are Bills fans’ IQs different? z test Example: z test Bills fans are smarter than average. Known vs. Unknown Population Standard Deviation • We used a z test to test the hypothesis that the mean of the population (i.e., Bills fans) that we sampled from is 100 But , we can only use a z test when the regular population standard deviation is known • Rarely do we actually know the population standard deviation Known vs. Unknown Population Standard Deviation If σ is unknown, we can’t compute σ M and therefore we can’t compute • What do we do if we can’t compute the standard error of the mean? • We must estimate it. • In order to estimate the standard error, we must estimate the 1 2 3 4 5 6 7
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population standard deviation. In order to estimate the standard error of the mean . . . . . . we must estimate the population standard deviation Estimating the Population Standard Deviation • What is the best estimate of the population standard deviation? Why is s a substitute for σ ? • We need to determine the parameters of the population of interest, assuming H 0 is true –This is the basis of tests of a population mean –The parameters for H 0 are adopted from the parameters of
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9_t_Test_Single_Mean_Outline - 1 2 t Test for a Single...

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