1. Null hypothesis: The results are due to chance.

2. Null hypothesis: The results are due to chance. This is the hypothesis you want to reject, since you are usually looking for an effect rather than looking for no effect. Thanks, Yolanda and Peggy!

3. Type I error: In reality, there is no effect, but you conclude that the results exceed chance level.

4. Null hypothesis: The results are due to chance. This is the hypothesis you want to reject, since you are usually looking for an effect rather than looking for no effect. Thanks, Yolanda and Peggy! Type I error: In reality, there is no effect, but you conclude that the results exceed chance level. Type II error: In reality, there is an effect, but you conclude that the results are due to chance. Thanks to Ixchel, Jennifer, Chauncey

5. Null hypothesis: The results are due to chance. This is the hypothesis you want to reject, since you are usually looking for an effect rather than looking for no effect. Thanks, Yolanda and Peggy! Type I error: In reality, there is no effect, but you conclude that the results exceed chance level. Type II error: In reality, there is an effect, but you conclude that the results are due to chance. Thanks to Ixchel, Jennifer, Chauncey Why p value at.05? Thanks, Erin, Carla, Lori and Jammie.

6. Tuesday, October 15 Probability and the Normal Curve

7. Number of HeadsProbability 0 1/64=.016 1 6/64=.094 215/64=.234 320/64=.312 415/64=.234 5 6/64=.094 6 1/64=.016 ___________ 64/64=1.00 What do you notice about this distribution?

8. Number of HeadsProbability 0 1/64=.016 1 6/64=.094 215/64=.234 320/64=.312 415/64=.234 5 6/64=.094 6 1/64=.016 ___________ 64/64=1.00 What do you notice about this distribution? Unimodal

9. Number of HeadsProbability 0 1/64=.016 1 6/64=.094 215/64=.234 320/64=.312 415/64=.234 5 6/64=.094 6 1/64=.016 ___________ 64/64=1.00 What do you notice about this distribution? Symmetrical

10. Number of HeadsProbability 0 1/64=.016 1 6/64=.094 215/64=.234 320/64=.312 415/64=.234 5 6/64=.094 6 1/64=.016 ___________ 64/64=1.00 What do you notice about this distribution? Two tails

11. GAUSS, Carl Friedrich 1777-1855 http://www.york.ac.uk/depts/maths/histstat/people/

12. f(X) = Where  = 3.1416 and e = 2.7183 1  2  e -(X -  ) / 2  22

13. Normal Distribution Unimodal Symmetrical 34.13% of area under curve is between µ and +1  34.13% of area under curve is between µ and -1  68.26% of area under curve is within 1  of µ. 95.44% of area under curve is within 2  of µ.

15. Some Problems If z = 1, what % of the normal curve lies above it? Below it? If z = -1.7, what % of the normal curve lies below it? What % of the curve lies between z = -.75 and z =.75? What is the z-score such that only 5% of the curve lies above it? In the SAT with µ=500 and  =100, what % of the population do you expect to score above 600? Above 750?

16. GMAT Problem from the Financial TimesFinancial Times What is the percentile rank of the mean GMAT score for Stanford? For Chicago? How would you state the difference between Stanford and Chicago? How would you characterize the difference between Stanford and Carnegie Mellon?