Introduction to t_Sp08_BBnocolor

Introduction to t_Sp08_BBnocolor - Outline Introduction to...

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1 The t-Distribution Outline • Introduction to the t-distribution • Normal distribution vs. t-distribution • 1 Sample t-test –Examp le Introduction • When do we ever know the standard deviation of the population ( σ )? – Can use σ M when testing hypotheses about the sampling means • 1-Sample Z test Introduction • When we don’t know σ , need to use the best estimator Estimated Standard Error (s M ) • Assumption: our sample is a random sample from the population – Variance of the sample should reflect the variance of the population
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2 Introduction • Potential problem – Biased estimate Population Distribution Sample Distribution Distribution Distribution of Means Introduction • We can calculate an unbiased estimate of the population variance i.e., an unbiased estimate of the standard error of the means 2 x x s s = 2 22 () (1 ) xx XM SS so r s nd f == Where SS = Sums of Squares Where SS = Sums of Squares & df = degrees of freedom df = degrees of freedom Normal Distribution vs. t- Distribution Leptokurtic = Bigger tails Normal distribution vs. t distribution • Shape of the t-distribution depends on degrees of freedom (df) – Entire “family” of t-distributions (each with a different df) • Shape of the normal distribution is unaffected by N
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This note was uploaded on 04/07/2008 for the course PSY 031 taught by Professor Dicorcia during the Spring '08 term at Tufts.

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Introduction to t_Sp08_BBnocolor - Outline Introduction to...

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