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28 Cards in this Set
- Front
- Back
Hypothesis
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A claim about a population parameter
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The Null Hypothesis
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(Ho)
- the status quo - begin with the assumption that the null hypothesis is true and try to disprove it |
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When do you reject the null hypothesis?
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If there is sufficient evidence against the status quo
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The Alternative Hypothesis
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(Ha)
- the opposite of the null hypothesis - challenges the status quo |
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Notation used for null hypothesis
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Always "="
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Notation used for alternative hypothesis
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≠ or < or >
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A hypothesis test
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- based on a sample
- the sample provides evidence to either support of reject Ho |
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If population is distributed normally....
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the sample mean is distributed normally
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For large samples from any distribution...
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the sample mean is distributed approximately normal by the Central Limit Theorem
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If it is unlikely to get a sample mean of _____ if in fact the population mean were ______, then?
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reject the null hypothesis
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What do you do before you start the test?
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Choose the level of significance (0.01, 0.05 or 0.10)
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What does the level of significance do?
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Defines the unlikely values of sample statistic if null hypothesis is true
- Rejection regions |
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What are the result possibilities, in terms of a jury trial?
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Correct - not guilty, innocent
- guilty, guilty Error - not guilty, guilty - guilty, innocent |
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What are the result possibilities, in terms of a hypothesis test?
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Ho True, Do not reject Ho = 1 - α
Ho True, Reject Ho = Type 1 Error (α) Ho False, Do not reject Ho = Type II Error (β) Ho False, Reject Ho = Power (1-β) |
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If α is small...
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then burden of proof/error is high
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If α is high....
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then β is low
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Type 1 Error
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(α): rejecting null when it is actually true
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Type II Error
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(β): not rejecting null when it is actually false
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What are the 7 steps in the Hypothesis Test?
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1. State Ho Parameter; represents the status quo and contains "="
2. State Ha parameter; challenges the status quo and contains "≠" or "<" or ">" 3. Choose α (level of significance) - determines rejection regions - consider risk of Type I and II errors 4. Choose sample size (n) 5. Select correct test statistic 6. Collect data and calculate sample stats and test stat Test statistic = (Sample Statistic - Null Ho Value)/Standard Error 7. Make the decision |
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What does the test statistic calculate?
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How many standard errors what you have observed is away from that stated in the null
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Test Statistic
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(Sample Statistic - Null Ho Value)/Standard Error
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What is the most common method to make the decision?
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The P Value Approach - sig in SPSS
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P Value
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The probability of obtaining a test statistic at least as extreme (≥ or ≤ or both) than the observed sample value, given Ho is true
- How likely is what you have observed if the null were true |
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Rule for P Value Approach
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If P is less than α, reject Ho
If p is ≥ α , DO NOT reject Ho --> If the p value is low, reject Ho |
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When do you use a Z test?
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When σ is known
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When do you use a t test?
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When σ is unknown
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What must we remember with the t test?
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Degrees of freedom (n-1)
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What do we use in a t test instead of σ?
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s
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