Spring 2010 Midterm 1 Review Slides

Spring 2010 Midterm 1 Review Slides - Statistical Inference...

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Statistical Inference Types of Test Exercises Econ203 - Midterm 1 Review Session Rafael Perez Ribas February 28, 2010 1

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Statistical Inference Types of Test Exercises Distributions Hypotheses Critical Statistic Distributions Every point estimate is a random variable, such as X S 2 X 1 X 2 S 2 1 = S 2 2 . First step is to obtain the standardized distribution of these r.v. (estimates) Then the test statistic, like z , t , F and 2 , is where your point estimated is located in the standardized distribution. 2
Statistical Inference Types of Test Exercises Distributions Hypotheses Critical Statistic Null and Alternative Hypotheses The Alternative Hypothesis, H 1 , is ALWAYS defined as what must be tested Is 1 > 2 ? Then H 1 : 1 > 2 The Null Hypothesis, H 0 , is ALWAYS the complement of H 1 Is 1 > 2 ? Then H 0 : 1 2 or H 0 : 1 = 2 3

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Statistical Inference Types of Test Exercises Distributions Hypotheses Critical Statistic Null and Alternative Hypotheses Question H 1 H 0 Point Estimate Rejection Region > 0? > 0 0 or = 0 X upper tail < 0? < 0 0 or = 0 X lower tail 6 = 0? 6 = 0 = 0 X upper and lower tails > 10? > 10 10 or = 10 X upper tail < 10? < 10 10 or = 10 X lower tail 6 = 10? 6 = 10 = 10 X upper and lower tails 1 > 2 ? 1 > 2 1 2 or 1 = 2 X 1 X 2 upper tail 1 < 2 ? 1 < 2 1 2 or 1 = 2 X 1 X 2 lower tail 1 6 = 2 ? 1 6 = 2 1 = 2 X 1 X 2 upper and lower tails 2 1 > 2 2 ? 2 1 = 2 2 > 1 2 1 = 2 2 1 or = 1 S 2 1 = S 2 2 upper tail 2 1 < 2 2 ? 2 1 = 2 2 < 1 2 1 = 2 2 1 or = 1 S 2 1 = S 2 2 lower tail 2 1 6 = 2 2 ? 2 1 = 2 2 6 = 1 2 1 = 2 2 = 1 S 2 1 = S 2 2 upper and lower tails 4
Statistical Inference Types of Test Exercises Distributions Hypotheses Critical Statistic Critical Statistic and Test Statistic They are not the same thing Test Statistic and p-values are given by the data that you have and depend on the hypothesized value

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