1. Thecriticalregionofatestis:

a)A subsetof the samplespace such thatthesample belongstoit isrejectedby thenull hypothesis.

b)A subsetof the samplespace suchthatifthesamplebelongstoit,thefalse hypothesisisrejected.

c)Such aregionofparametric space thatifthe parameterbelongstoit,the nullhypothesisisrejected.

d)Such aregionofparametric space thatiftheparameterbelongstoit,the falsehypothesisisrejected.

2. Thesignificance levelofahypothesis test :

a)

It is usuallysmalland fixedby the researcheror agenerallyacceptedcovenant.

b)

It givestheprobabilityof declaringtheresultof a test significant,when thisisfalse.

c)

DecreasingincreasesthelikelihoodoftypeII error.

(d)

All of theaboveistrue.

(c)

All of theaboveisfalse.

3.In ahypothesis contrast theamountofis:

a)A smallnumber.

b)Fixedbeforecontrasting.

c)The probabilityofrejectingthenull hypothesis.

d)The probabilityof errorinrejectingthealternative hypothesis.

e)Known whenextractingthe sampleandcalculatingtheexperimentalstatistic.

4.Only oneofthefollowingphrasescouldeverbe found astheconclusionofascientific study. Which one isit?

a.Treatment had asignificantlygreater effectthanplacebo(p-0.75)

b.Treatment had asignificantlyless effectthanplacebo(p-0.25)

c.Treatment didnotproduce aresultotherthanplacebo(p<0.001)

d.Treatment had asignificantlyless effectthanplacebo(p-0.99)

e.Significant differencesbetweenplaceboandtreatmentwereobserved(p<0.001)

5.The nullhypothesisoftheVarianceAnalysis states:

a)There are differencesbetween the samplemeans.

b)There areno differencesbetweenthe means of thesubpopulations.

c)There are differencesbetweenthe means of thesubpopulations.

d)There areno differencesbetweenthe samplemeans.

ITEM II. An electric company manufactures cell phone batteries that last approximately normally with an average of 800hours and a standarddeviationof40hours. Arandomsampleof30batterieshasanaveragedurationof785hours.

a)Does the data show enough evidence to say that the average duration is less than 800? Useasignificance level of5%.

b)Find theP-value

ITEM III. In Metro stores 70% ofpurchasesareinfoodandbeverages. Ifrandomsamplesof200 purchases areselected.Calculateandinterpret:

a)Between which symmetrical limits around the true percentage of food and beverage purchases willfall 99% ofthe samplepercentages?

b)How many food shoppingsampleswe would need ifweapplieda3%marginof error.

ITEM IV. A companywantsto competetowin a contractwith thegovernmentasa concrete supplier; one of the requirement is the resistance to the compression of the concrete within 28 days of the mixturebeingprepared. Thewinningcompanysaysthatit maintains excellent quality controls in its concrete and as such there is a very low variance in compressionresistance, in the order of 16kgf²/cm⁴; but when doing inINTEC a higher variance of 25 kgf²/cm4 cm⁴ ;

a) is theresufficientstatisticalevidenceto consider thattheprovider islyingandactuallythe standarddeviationisDIFFERENTto16 kgf²/cm⁴

c) Writing the hypothesis test, indicatingwhether it should be proof of one or two queues toanswerthequestion.

d) Determine by means of the square ji test statistic whether null hi poresis isaccepted or rejectedandwhatwouldbe theconsequenceofthe resultobtainedforthequestion.

THEME V. The Directorate General of Public Procurement has registered about 6600 suppliers oftheState,withthefollowingcomposition:Natural Person1650suppliers, Medium Enterprise 1200 suppliers, Gran Empresa 1055 suppliers and Microenterprises 2695 suppliers.

ThesurveyorcompanyCAC hasbeen chosentosampleabout the perceptionofStateSuppliers abouttheGoverningInstitution.

The company uses proportional tiered random sampling. Youasasamplingspecialistforthesurveyer:

a)What isthestudypopulation?

b)Determine thesamplesizebysettingstrataorsubgroups