# Statistics Final Exam Review Sample Essay

Rejecting the nothing may be a error = P –value

ONE Sample
3 expressions
T. Dist. rt ( t. sample size – 1 “df” ) – & gt ; alternative that mu is bigger than a 1 – T. Dist. rt ( t. sample size – 1 ) – & gt ; mu is less than a T. Dist. 2t ( t. samplesize – 1 ) – & gt ; non equal to

P & lt ; important degree reject the nothing

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NEVER accept void

TWO Sample
straight acquire the p-value
opportunity that under the void hypthoesis. you have a difference in the sample mean that is as extreme or more as what you have now. If that chance is little. it is something in the nature non due to opportunity.

* Paired: T. Test ( sample 1. sample 2. # of dress suits. 1 )
* non equal to: figure of dress suits = 2
* greater than or less than: figure of dress suits = 1
* Type 1 = paired informations ( ex: every UNC Master in Business student’s wage before they entered the plan and wages after alumnus ) * wages have a important addition after Master in Business?

* Mugwump: T. Test ( sample 1. sample 2. # dress suits. 2 )
* Type 2 = independent ( antique: UNC mbas vs. DUKE Master in Business )

* Regression Coefficient:

* Null hypothesis: THIS arrested development coefficient = 0
* alternate hypothesis: THIS peculiar arrested development coefficient of involvement is non 0 *
* ( driver’s p-value and coefficient in ANOVA )

* THIS driver’s p-value is less than important degree. so the driver has a important impact on the result. *
* ** for each person driver

* Hypothesis trial on a arrested development theoretical account as a whole:

* Null: All incline coefficients = 0 ( R square being nothing ) * Alt: At least ONE incline coefficient is non equal to zero ( R square greater than 0 ) *
* P-value is SIGNIFICANCE F on the ANOVA.

IF significance F & lt ; important degree. arrested development theoretical account is important as a whole. *

* Hypothesis trials for full versus Partial arrested development theoretical accounts: *
* Partial theoretical account is worse than the full theoretical account
* 2 theoretical accounts on the same information where one model’s drivers are a subset of another model’s drivers. *
* full theoretical account – MUST HAVE MORE DRIVERS THAN THE OTHER AND MUST CONTAIN ALL THE DRIVERS IN THE PARTIAL MODEL AND SHOULD BE BASED ON SAME DATA *
* Partial f trial:
* Null: partial theoretical account is every bit good as full theoretical account ( R square full = R square partial ) * Alt: Partial theoretical account is less explanatory than full ( R square full & gt ; R square partial ) *
more drivers ever increases R square

* 1 ) First find Partial F value ( expression )

* denominator:
* ( 1 – R square ) per centum non explained
* / ( df ) of residuary: sample size – full theoretical account – 1
* ITS IN THE ANOVA OUTPUT DF full. residuary and variable. . pick RESIDUAL *
* Find p-value

* 2 ) F. Dist. rt ( partial F. # variables removed. df residuary ) *

* Hypothesis trials for autocorrelation in remainders:

* DW statistic
* DW = SUMXMY2 ( all but first remainders. all but last ) / SUMSQ ( all remainders ) *

* T = observations
* K =
* DW & lt ; deciliter: positive autocorrelation

* CONFIDENCE INTERVAL FOR POPULATION MEAN

* simple sample
* with certain certainty. my population is between these two values. *
* MoE = critical T clip standard mistake ( calculator of mistake of sample mean ) * SE = stdev. s/ SQRT

* critical T = T. INV. 2T ( significance degree. df )
* SE = stdev. s/sqrt
* Exact moe = critical T * Se
* Exact: sample mean + – moe

* approximative 95 % assurance: Use 2 for MOE and it is 2 * Se *

* Confidence interval for population proportion

* Indicator variables
* 1 = falls within class
* 0 = does non
* Approximate & amp ; conservative 95 % = 1 / SQRT ( samplesize ( * Confidence interval: sample prop + – MoE

* moE 10 % how many pupils I need to inquire?
* . 10 = 1/SQRT ( ten )

* Confidence interval for two populations’ average difference *
* Approximate 95 % = 2* SQRT ( stdevs. 1… )
* For INDEPENDENT

Assurance interval for mated 2 populations’ average difference *
* for PAIRED informations:

* Take difference between each brace and throw away original informations *

* Normal distribution estimations:
* 2/3 of the opportunity that it falls between -1 +1 standard divergence * 95 % that it stands between -2 and +2

* Interpretation of arrested development end product elements
* Lags in clip series arrested development
* Standard format of a prognosis expression
* Cause. symptom and redress of multiocrrelation
* autocorrelation ( losing a driver. driver should be at that place )
* symptom: clear spiel. DW low plenty
* redress: include driver

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