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Ch. 14 part 2

# Ch. 14 part 2 - Tests of Significance The second inference...

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Tests of Significance The second inference method discussed in Chapter 14 is called tests of significance . When we conduct these tests, we’re going to have some claim about our population, and we’re going to see if the data supports or refutes that claim. 1 Chapter 14

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Tests of Significance Example: I claim that I make 80% of my field goal kicks in football. You do not believe me, so you ask me to go to the stadium and kick 20 field goals. I only make 8 out of the 20 field goals. 2 Chapter 14
Tests of Significance If you use the BIN(20, 0.8) distribution, the probability I would make 8 or fewer field goals is only about 0.0001. If my claim is true, I would make 8 field goals or less once in 10,000 tries. This should convince you that my initial claim is not true. 3 Chapter 14

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In short: An outcome that would rarely happen if a claim was true is good evidence that the claim is not true . For our tests of significance, we will think along these lines (and use the assumptions we have talked about). 4 Chapter 14 Stating Hypotheses Null Hypothesis, H 0
Stating Hypotheses Null Hypothesis, H 0 Definition : The initial claim tested by a statistical test is called the null hypothesis . This is typically denoted as “H o ”. Example : In a court trial, the rule of thumb is “innocent until proven guilty.” Thus, the null hypothesis for a trial is “The person is innocent.” 5 Chapter 14

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Chapter 14 6 The statement being tested in a statistical test is called the null hypothesis . The test is designed to assess the strength of evidence against the null hypothesis. Usually the null hypothesis is a statement of “no effect” or “no difference”, or it is a statement of equality. Stating Hypotheses Null Hypothesis, H 0
Tests of Significance When performing a hypothesis test, we assume that the null hypothesis is true until we have sufficient evidence against it. The null hypothesis is the claim that a test of significance is trying to disprove (like my free throw shooting). Along with the null hypothesis, there will be another claim which we are trying to prove . This claim is called the alternative hypothesis (denoted using “H a ”). 7 Chapter 14

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Chapter 14 8 The statement we are trying to find evidence for is called the alternative hypothesis . Usually the alternative hypothesis is a statement of “there is an effect” or “there is a difference”, or it is a statement of inequality. The alternative hypothesis should express the hopes or suspicions we bring to the data. It is cheating to first look at the data and then frame H a to fit what the data show.
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