BMGT230B Sheet - All the info for First Exam PDF

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All the info for First Exam...

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BMGT230B Exam #2 Chapter 8 • Random Variable: value is based on the outcome of a random event o Discrete – list all outcome o Continuous – any value • Expected Value: (population mean) 𝜇 = 𝐸 𝑥 = !𝑥 ∗ 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 • Variance is SD2 𝜎 ! = 𝑉𝑎𝑟 𝑋 = ! 𝑥 − 𝜇 ! 𝑃(𝑥) o 𝑉𝑎𝑟 𝑋 ± 𝑐 = !𝑉𝑎𝑟 𝑋 𝑉𝑎𝑟 𝑎𝑋 = ! 𝑎 ! 𝑉𝑎𝑟 𝑋 𝑉𝑎𝑟 𝑋 ± 𝑌 = !𝑉𝑎𝑟(𝑋) ± 𝑉𝑎𝑟(𝑌) o 𝐸 𝑋 ± 𝑐 = !𝐸 𝑋 ± 𝑐 𝐸 𝑎𝑋 = !𝑎𝐸 𝑋 𝐸 𝑋 ± 𝑌 = !𝐸 𝑋 ± 𝐸 𝑌 o 𝑆𝐷 𝑋 ± 𝑐 = !𝑆𝐷 𝑋 𝑆𝐷 𝑎𝑋 = |𝑎|𝑆𝐷(𝑋) 𝑆𝐷 𝑋 ± 𝑌 = ! 𝑉𝑎𝑟(𝑋) ± 𝑉𝑎𝑟(𝑌) • Geometric probability model (how many trials until achieve first success) “unlimited number of trials” !

Expected Value: 𝜇 = !, Standard Deviation 𝜎 =

o •

! !!

Binomial probability model – probability exactly X successes is the same; “specified number of trials”, success/fail, independent o Expected Value: 𝜇 = 𝑛𝑝, Standard Deviation 𝜎 = 𝑛𝑝𝑞 Binompdf(trials, probability, value) 𝑃 𝑋 =

o

!! !! !!! !

𝑝 ! 𝑞 !!! where x is the number of successes, p is the probability of success

per trial, q is the probability of failure per trial and n is the sample size 1-binomcdf(trials, probability, value): u-x/sqrt(npq) ! Continuity correction: if more than x, add .5; if less than x, subtract .5 Normal Model – appropriate for distributions whose shapes are unimodal and roughly symmetric (bell shaped curves) 𝑁(𝜇, 𝜎) o 68 – 95 – 99.7 (1 SD, 2 SD, 3 SD) 0 – .15 – 2.5 – 16 – 50 – 84 – 97.5 – 99.85 o

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Chapter 9 • CLT tells us that the sampling distribution of both sample proportion and sample mean = Normal !" ; if !

there is no estimate, use .5

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(Also used for Standard Error) Standard Deviation (proportion) 𝜎 =

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CI = Estimate ± Margin of Error = 𝑝! ± 𝑍 ∗

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(CI, Z*) – (90%, 1.645), (95%, 1.96), (98%, 2.326), (99% 2.576) Increase confidence interval, larger margin of error Assumption: SRS, 10%, Success/Fail With 95% confidence, the proportion of people in the population is between M1% and M2% o 95% of samples of this size will produce confidence intervals capturing true population Sampling Error – is the deviation from the true characteristics for a sample

•

!!! !

Sampling size for desired 𝑀𝐸 = 𝑍 ∗

o

!" !

!∗

!𝑠𝑜!𝑛 = (!" )! (𝑝𝑞)

Chapter 10 • State the hypothesis, test statistic, p value, compare alpha • 𝐻! : 𝐸𝑓𝑓𝑒𝑐𝑡!𝑖𝑠!𝑑𝑢𝑒!𝑡𝑜!𝑐ℎ𝑎𝑛𝑐𝑒 𝐻! : 𝐸𝑓𝑓𝑒𝑐𝑡!𝑖𝑠!𝑑𝑢𝑒!𝑐𝑙𝑎𝑖𝑚 alpha by 2) !!! • 𝑍 = ! ! !! pα fail to reject the null

(one tail divide

! ! !

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Fail to reject – not enough evidence that proportion is different than population Reliability – smaller p value, stronger evidence against null, more confidence Magnitude or size is how relevant to real life the phenomenon is; p value does not measure α↓ β↑ Power↓ n↑ α↓ β↓ Power↑ Power is 1- β and is the ability to accept 𝐻! when 𝐻! is true α low and Power low, more possibility for Type II Error

Chapter 11 ! • Sampling distribution of mean: 𝑆𝐸 𝑦 = !and 𝑀𝐸 = 𝑡∗!!!𝑆𝐸(𝑦) !

!

(𝑥! − 𝑥)! OR Stat, Edit, L1… Stat, Calc, 1-Var Stats

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𝑠=

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Assumptions: SRS, 10%, Nearly Normal (check histogram) !!!! and use 𝑡𝑐𝑑𝑓( 𝑃𝑣𝑎𝑙𝑢𝑒!𝑜𝑟 −𝑒 !! , 𝑃𝑣𝑎𝑙𝑢𝑒!𝑜𝑟!𝑒 !! , 𝑑𝑓) Test hypothesis: 𝑡!!! =

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T degrees of freedom – increases as it approaches Normal distribution, fatter tails, narrower center ! ! ∗! Sample Size 𝑚 = 𝑍 ∗ ! !!!!𝒐𝒓!!!!!𝑛! = ( )!

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If the sample calculated is less than 60, round up and continue using the T by using n-1 and finding df ! !∗!!!! ! ) 𝑀𝐸 = 𝑡∗!!! !!!!!𝒐𝒓!!!!!!!!𝑛! = (

•

!!!

!"(!)

!"

!

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