Null hypothesis: The results are due to chance.. Null hypothesis: The results are due to chance. This is the hypothesis you want to reject, since you.

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Presentation transcript:

Null hypothesis: The results are due to chance.

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.

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

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.

Tuesday, October 15 Probability and the Normal Curve

Number of HeadsProbability 0 1/64= /64= /64= /64= /64= /64= /64=.016 ___________ 64/64=1.00 What do you notice about this distribution?

Number of HeadsProbability 0 1/64= /64= /64= /64= /64= /64= /64=.016 ___________ 64/64=1.00 What do you notice about this distribution? Unimodal

Number of HeadsProbability 0 1/64= /64= /64= /64= /64= /64= /64=.016 ___________ 64/64=1.00 What do you notice about this distribution? Symmetrical

Number of HeadsProbability 0 1/64= /64= /64= /64= /64= /64= /64=.016 ___________ 64/64=1.00 What do you notice about this distribution? Two tails

GAUSS, Carl Friedrich

f(X) = Where  = and e =  2  e -(X -  ) / 2  22

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 % of area under curve is within 2  of µ.

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?

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?