{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

More Hypothesis Testing

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

Info icon This preview shows pages 1–17. Sign up to view the full content.

View Full Document Right Arrow Icon
More Hypothesis Testing
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 2
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”
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 4
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
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 6
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
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Comparing Two Proportions Chapter 22
Image of page 8
Z Test for Differences in Two Proportions
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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 - -
Image of page 10
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
Image of page 11

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Example
Image of page 12
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?
Image of page 13

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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.
Image of page 14
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:
Image of page 15

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Critical Value Z*
Image of page 16
Image of page 17
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern