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More Hypothesis Testing

# More Hypothesis Testing - More Hypothesis Testing P-Values...

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More Hypothesis Testing

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P-Values The P-value is not the probability the null hypothesis is true Is the Conditional Probability P(observed Statistic I Ho) The lower the p-value the more comfortable you feel about your decision to reject the null hypothesis
P-Values Cont. We can define a “rare event” arbitrarily by setting a threshold for our P-value If our P-value falls below the point, we’ll reject the null hypothesis We call such results statistically significant The threshold is called an alpha level Alpha level is the significance level When we reject the null hypothesis we say that the event is “significant at that level”

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Different Confidence Levels = Different Critical Value Alpha Level 1-Sided 2 sided .05 1.645 1.96 .01 2.33 2.576 .001 3.09 3.29
Type 1 and 2 Errors Type 1 Error Occurs when the null hypothesis is T and we mistakenly reject it False positive Type 2 Error Occurs when the null hypothesis is false, but we fail to reject it False negative

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More on Error When you choose an alpha level you are setting the probability of a Type 1 error to the alpha level The truth Your decisio n Ho True Ho False Reject Ho Type 1 Fail to reject Ho Type 2
Power Beta (β) - the probability that a test fails to reject a false null hypothesis The power of the test is the probability that is correctly rejects a false null hypothesis Want a higher power Power = 1-β

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Comparing Two Proportions Chapter 22
Z Test for Differences in Two Proportions

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Z Test for Difference in Two Proportions 1. Assumptions Populations Are Independent Normal Approximation can be used 10 ) p ˆ 1 ( n and 10 p ˆ n 10 ) p ˆ 1 ( n and 10 p ˆ n 2 2 2 2 1 1 1 1 - -
Z Test for Difference in Two Proportions 1. Assumptions Populations Are Independent Normal Approximation can be used 2. Z-Test Statistic for Two Proportions 10 ) p ˆ 1 ( n and 10 p ˆ n 10 ) p ˆ 1 ( n and 10 p ˆ n 2 2 2 2 1 1 1 1 - - ( 29 ( 29 2 1 2 1 2 1 2 1 n n X X p ˆ where n 1 n 1 p ˆ 1 p ˆ p ˆ p ˆ Z + + = + - - 2245

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Example
Two Proportion Z Test Example Is drug use running rampant? Students at SFCC were asked if they have ever smoked marijuana. 92 out of 122 males responded yes compared to 60 out of 96 females. Is the population proportion of males who have ever smoked marijuana more than that of females?

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Checking the Assumption* 10 36 ) 625 . 0 1 ( 96 or 10 ) p ˆ 1 ( n and 10 60 ) 625 . 0 ( 96 or 10 p ˆ n 10 30 ) 754 . 0 1 ( 122 or 10 ) p ˆ 1 ( n and 10 92 ) 754 . 0 ( 122 or 10 p ˆ n 2 2 2 2 1 1 1 1 = - - = = - - = So the sample sizes are large enough.
Two Proportion Z Test Solution H 0 : p m = p f H a : p m p f n m = 122 n f = 96 Test Statistic: P-value: P-value: Decision: Decision: Conclusion: Conclusion:

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Critical Value Z*
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