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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 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 ± ² 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 ± ² 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 ³ ± X 2 upper tail ± 1 < ± 2 ? ± 1 < ± 2 ± 1 ² ± 2 or ± 1 = ± 2 ± X 1 ³ ± X 2 lower tail ± 1 6 = ± 2 ? ± 1 6 = ± 2 ± 1 = ± 2 ± X 1 ³ ± X 2 upper and lower tails ² 2 1 > ² 2 2 ? ² 2 1 2 2 > 1 ² 2 1 2 2 ± 1 or = 1 S 2 1 = S 2 2 upper tail ² 2 1 < ² 2 2 ? ² 2 1 2 2 < 1 ² 2 1 2 2 ² 1 or = 1 S 2 1 = S 2 2 lower tail ² 2 1 6 = ² 2 2 ? ² 2 1 2 2 6 = 1 ² 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

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

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