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Econ 281 - Chapter 5 Hypothesis Testing

# Econ 281 - Chapter 5 Hypothesis Testing - Chapter 5...

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1 Chapter 5: Hypothesis Testing Introduction to Econometrics Econ 281 Spring Quarter 2007

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2 Hypothesis testing in the simple linear Regression Model Let’s assume we ran a regression of Test Scores on the Student Teacher Ratio and obtained the following results Can we be sure that the true (population) parameter is not zero? We use hypothesis testing to obtain an answer to this question STR TestScore - = 28 . 2 9 . 698 1 β
3 Hypothesis Testing The first thing to do in Hypothesis Testing is to formulate TWO MUTUALLY EXCLUSIVE hypotheses The Null Hypothesis The hypothesis we are interested in – Denoted by H 0 The Alternative Hypothesis – The hypothesis if H 0 is not true – Denoted by H A

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4 Hypothesis Testing Let’s start with a simple example and test the hypothesis that a population mean is equal to a specific number In this case our H 0 would be 0 : 0 H X H μ μ = Value of population mean under Null Hypothesis
5 Hypothesis Testing Our alternative Hypothesis can take two forms One-Sided Two-Sided Two-Sided alternative hypothesis One side alternative hypothesis 0 : H X A H μ μ 0 : H X A H μ μ

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6 Hypothesis Testing Now we take a random sample and calculate the value of the sample mean Most likely it will differ from the value specified in H 0 . Why? Two reasons The Null Hypothesis is false Random Sampling We CANNOT distinguish between the two with certainty
7 Hypothesis Testing What can we do? We can ask “What is the probability of observing this particular value of the sample mean if the Null Hypothesis is in fact true?” We call this the p-value or significance probability Let’s look at an example

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8 Hypothesis Testing: Example Assume the Bulls finish the season 50-32 This implies the true population mean is 0.61 Assume we take a sample of 30 games and calculate a sample mean of .55 We formulate a Null Hypothesis that the true mean is actually 0.2 Our one-sided alternative hypothesis is that the true mean is greater We get a p-value of less than 1 percent!! This makes it very unlikely that the H 0 is true!!!
9 Hypothesis Testing Question: How are p-values calculated?

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