first claim, then collect data.the null hypothesis: always what we test, and assume it's true. gives us a value for parameter, statement of equality. miu =, <=, >= 10 alpha increase, boundary lines move toward the center.three different natures of the test1.two sided test assume change could have happened in either direction. assume evidence fall away from the center of the distribution. expected data value to fall 95% area. greater than or less than current claimed value, in the center of the distribution.two rejection zonesalpha risks determines boundary lines, critical valuesalpha will be divided by two.if we reject, alternative hypothesis says evidence is not going to be within the region.the null hypothesis says, the value falls within the LOC somewhere. if the evidence fall within, we say do not reject null hypothesis. keep null hypothesis is true. alternative hypothesis, evidence falls outside of the LOC, either greater than, or less than the hypothesis value. there is enough evidence to support.2.one sided test, right 3.left,just a increase, or decreasewhen we are interested in deviation in which side. ----------------you first give a claim, then, you collect data. -----------------test assume to be true- within LOCthe null hypothesis test is what we always test. assumed to be true.defendants in trail. even if your claim is in alternative, you always test nullnull hypothesis give value for parameter, statement of equality.equal to, less than and equal to, greater than, and equal tothe equal value will work everytimez=(xbar-miu)/(sigma/sqrt(n))null hypothesis always assume to be true--------nature of the test: one tail to two tail.-----------3(a) always be miuclaim is always about parameter-----------his claim is an alternative hypothesis (Ha) find evidence far enough to the left of 2 to be statistically significant. null would be opposite from the claim. test the null hypothesis. assume the opposite is true.assume null hypothesis is true. given Ha miu <2test Ho miu >= 2"<" we'll have a negative CV value, alpha regoin determine boundary line. show sample mean (xbar) definitely fall less than the critical value, enough evidence, show the average is significantly less than 2reject null hypothesisif he find x bar inside loc, within the margin of error, do not reject the null hypo, not enough evidence-move beyond the boundary of the cv, -------------------------reduced--one tail.any affect--two tailsreduced--less than-------------------------nothing mentioned about "one tail"people can do two tail test, two tail not equal to one tail stronger greateralternative or null-------------------------critical value for two tail test boundary linebased on alpha risk toward or away middle of the curve based on value of alphaalpha increase, towarddecrease, away(toward tail) less area of the tailarea of the tail, alpha regionevidence fall beyond the fences, reject the null, isn't enough evidence to say significanttest statisticp valuedon't come up with CVjump in evidencetest statistics(Ho) any numerical valuebut when turn in to z, t score, middle becomes zerowhat is the z score or t score,location of the evidence--the test of the statistics,z=deviation/standard errorhow far away is the evidence from the middle(the claimed value)then, divided by the units (every curve changes bases on standard error)standard error decreases, the curve taller and narrowerstandard error wider, shorter, with more variation this particular curvethe unit depend on standard errorthe probability of being more extreme than the evidence assuming the null is true (why? because based on this curve based on this distribution centered at the null hypothesis), is the p value, the area under the curvet.dis--t score, t.dist (-t,df,true)normdist--z scoreleft tail test--normsdist(-z)dist--area under the curvehow do you get probability-- distribution functionhow do you get critical value--inverse functionif you have sigma or notsigma, normsdist, test statistics correspond to the evidencepositive, negativegreater than; 1-normsdist (+z)t.dist.rt(t,df)two tail test: (Ha) not equal to two tail test: alpha/2double p value, then, compare to all the alphapositive:(1-normsdist(+z))*2t.dist.2t (t,df)negative:normsdist(-z)*2t.dist.2t(t,df)inverse function give you CVtest statistics you need a formula--------------------------------------------------p value--innocentsmall p value--stronger evidence to reject-juryenough evidence to reject the nullnot enough evidence to reject the nullnot accpetp > alpha riskp < alpha riskp small, reject null, something increased, decreased, or changed. there is enough evidence, statistically significantly change has occur. different from what it assumed to be. smaller, strong evidence, to reject the null, therefore accept alternative, more power to reject"reduces the risk"--changeshow small, smaller than the alpha risksmall p value, stronger evidence to reject null.-------------------------------------------------------5% assume, alpha risk, if they don't offer.if you reject the null, you accept alternativesor then, you keep the null.-------dist function for zright T alternative >null <=p value, evidence, "z"sright: 1-normsdist(+z)t.dist.rt(+t,df)left tail test: Ha < Ho >= alpha risk, on the left tail,negative test statistics=normsdist (-z)=t.dist(-t,df,true)two tail test: Ha not equal to, Ho equal to, alpha/2 in each tail, like a level of confidence, to compare to the p value, because you are compare the entire alpha risk, you have to double (alpha/2) *2-z, 2*(normsdist(-z))-t, =t.dist.2t(absolute value of t(excel doesn't accept negative t value), df)evidence fall greater than the middle of the curve, positive z,tpositive or negative t=2* (1-normsdist(+z))=t.dist.2t(absolute t, df)all "z"s, what function are you going to use.p value, not reject null, p, alpha risk--reject, not rejectp smaller than alpha, rejectp larger than alpha, do not rejectNEVER 1-normsinvRight tail:What’s really happening, where 44(evidence) falls. Add me, positive cv, based on alpha risk. Does 44 fall in rejection zone, or not rejection zone. Until come out with CV, we then know. Critical z score, inv function. How to come up with critical value. =normsinv(1-alpha); never 1-normsinv, 1- put in the probability.Positive critical value—normsinv(1-alpha)Negative cv(left)—normsinv(alpha)Two tail test—normsinv(alpha/2) , then add “+”,”-“signTest statistics: where 44 falls?Z=(44-42)/(13/sqrt31)42, claimed