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Chap. 22 - Lecture Notes - SC

# Chap. 22 - Lecture Notes - SC - Chapter 22 Tests of...

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Chapter 22 Tests of Significance

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Significance Tests Statistical inference uses data from a sample to draw conclusions about a population. We saw one method of doing this previously with Statistical tests ask if sample data give good evidence a claim. Example: I claimed that I had a standard card deck, you believe there is evidence against my claim based on the sample of cards you took.
Reasoning Statistical tests use the reasoning that: An outcome that is very unlikely if a claim is true is good evidence that the claim is not true. Another Example: If someone claims to make 80% of their free throws in basketball, and then only makes 6 out of 20, you may start to question whether his claim of 80% is true!

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Hypothesis Tests Statistical Tests are also known as We want to test a hypothesis (statement) about the value of a Statistical Hypotheses:
Hypothesis Tests A checks sample data against a claim or assumption about the population. The claim or assumption being tested is called the Example: The statement we hope or suspect is true instead of H 0 is called the Example:

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Hypothesis Tests A looks for evidence against the null hypothesis and in favor of the alternative hypothesis. If the , we stop assuming the null hypothesis and find in favor of the alternative hypothesis. If the , we continue to assume the null hypothesis. At the end of a hypothesis test we either have
Hypotheses The alternative hypothesis (H a ) can take three forms based on what we want to prove is true. (# is often denoted p o ) One-sided alternative: Two-sided alternative:

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Consider the Deck of Cards Let p = We assumed half the cards are red: But we suspect the alternative: The sample evidence is
We conduct a hypothesis test under the assumption that H 0 is true and the claim we believe, H a

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Chap. 22 - Lecture Notes - SC - Chapter 22 Tests of...

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