Statistics for Journalism

Transcription

1 Statstcs for Jouralsm Fal Eam Studet: Group: Date: Mark the correct aswer wth a X below for each part of Questo 1. Questo 1 a) 1 b) 1 c) 1 d) 1 e) Correct aswer v 1. a) The followg table shows formato about the daly sales of ewspapers for each 1000 habtats of 8 Spash Commutes ad the ecoomc producto of the commuty based o the PIB (Producto Iterór Bruto) per resdet. PIB Sales Fuete: INE. Auaro Estadístco. Supposg a lear relato betwee these varables, we obta the followg regresso le whch eplas the umber of papers sold per 1000 habtats terms of the PIB per resdet 1000 s of euros: y= What would be the predcted sales a commuty wth PIB per resdet equal to euros? a eamples b eamples for each 1000 habtats c eamples d eamples for each 1000 resdets b) I a recet opo poll for the Suday Epress, 11% or people sad that they would vote for the UK Idepedece Party (UKIP) whch wshes the UK to leave Europe. Assumg these results reflect the opo of UK voters, f three voters are chose at radom, what s the probablty (to 3 decmal places) that at least oe of them would vote for the UKIP?. 0,95 1

2 . 0,110. 0,61 v. 0,999 c) The followg resposes come from a late 011 survey by the BBC about Lodoers opos o the Olympcs. Q3. How ected are you about the Olympcs takg place Lodo? Opo Percetage Very ected 30 Farly eted 35 Not very ected 18 Not at all ected 16 Do t kow 01 The survey was carred out usg a sample of 1000 Lodoers. Appromately how may people were farly ected or more? v. 650 d) The followg dagram comes from a 01 artcle the Facal Tmes ettled Vce Rehart does QE really work? ad shows the relato betwee short ad log term terest rates. Whch oe of the followg statemets s correct?. The correlato betwee short ad log term terest rates s egatve ad the covarace s egatve.. The tercept of the regresso le s postve ad the correlato betwee short ad log term terest rates s postve.. The tercept of the regresso le s egatve ad the correlato betwee short ad log term terest rates s postve. v. Noe of the prevous aswers.

3 e) I a recet survey, 100 ctzes of Greece, Spa ad the UK were asked whether they thought the Euro would survve the curret crss. Ther reples are summarzed the followg table. Respose Coutry Greece Spa UK Yes No Do t kow Whch of the followg statemets s correct?. The proporto of people the sample who thk the Euro wll survve s If a perso s chose at radom from the sample, the evets Do t kow ad Come from Spa are depedet.. If a perso chose at radom from the sample comes from a coutry wth the Euro zoe (Greece or Spa), the probablty that they thk the Euro wll ot survve s v. The probablty that a radomly chose perso, who thks the Euro wll ot survve, comes from Spa s 0.05?. I the latest Barometer of the CIS (Aprl 01), oe of the party leaders acheved a pass ratg of 5. The hghest rated was Rosa Dez who acheved a mea ratg of 4.47 wth a stadard devato of.51. The secod rated was Alfredo Perez Rubalcaba wth a mea ratg of 4.11 ad a stadard devato of.74. a. What s the probablty that a radomly chose perso rates Rosa Dez at over 5? (0.75 pots) b. Calculate the probablty that a radomly chose perso gves Alfredo Perez Rubalcaba a ratg of eactly 5. (0.5 pots) c. If three people are chose at radom, what s the probablty that oe of them gve Rosa Dez a pass ratg? (0.5 pots) d. I a sample of 100 people, what would be the epected umber of people who would gve pass grades to Rosa Dez? (0.75 pots) 3

4 3. The followg artcle comes from the MercoPress South Atlatc News Agecy o 3 rd Aprl 01. YPF sezure approved by 6% of Argetes, accordg to opo poll The recet decso by Presdet Crsta Feradez to seze a majorty stake YPF from Spa s Repsol has the approval of 6% of Argetes, whle 3% dsagree accordg to a publc opo poll from Polarquía publshed the Suday edto of La Naco. The poll shows that 6% the captal Bueos Ares ad dfferet ctes of the coutry are very much agreemet wth the decso ad 36% are agreemet. The decso has soured log establshed relatos betwee Argeta ad Spa that has promsed reprsals, ad demads full compesato f the decso s ot revewed. Aother 3% sad they were dsagreemet wth atoalzato, ad 8% rejected pot blak the decso. Asked about the possble mpacts o the Argete ecoomy, 49% sad the decso was postve ad 47% admtted to fears that t would affect egatvely the mage of Argeta overseas. The poll also showed that 49% of resdets from the captal Bueos Ares support the atoalzato, eve whe the mayor of the cty ad the ma oppoet of Crsta Feradez, Maurco Macr rejected the sezure ad wared that the lawmakers from hs party would vote agast the tatve Cogress. I the rest of the coutry the decso had the support of 66% of tervews, where four out of te sad they were very much agreemet. The poll cluded phoe tervews wth over 18 years of age ad the forty ma ctes of Argeta. a. Calculate a 95% cofdece terval for the true proporto of Argetes who thk that the mpact of the atoalzato wll be postve. Is there ay evdece (at a 5% sgfcace level) that ths proporto s dfferet from 50%? Epla your cocluso. (1.5 pots) b. Is there ay evdece that more tha 60% of Argetes approve of the atoalzato of Repsol YPF? Carry out the test at a sgfcace level of 5% ad epla your coclusos. (1.0 pots) 4

5 5 CHULETARIO OFICIAL ) Resultados báscos (basados e ua muestra de tamaño ) X 1 1 ) ( S ) y ( y Cov(X,Y) 1 S S y Cov(X,Y) r(x,y) ) Regresó La recta de mímos cuadrados es y = a + b dode y S S r(x,y) S Cov(X,Y) b ) (b y a ) Itervalos de cofaza de 95% (basada e ua muestra de tamaño N) para a) La meda de ua poblacó ormal (varaza coocda) b) Ua proporcó

6 v) Cotrastes de hpótess de vel de sgfcacó. Z represeta el puto tal que P(Z <Z )=1-dode Z tee ua dstrbucó ormal estádar. a) para la meda de ua poblacó ormal (varaza coocda) H 0 H 1 Regó de rechazo = 0 < 0 = 0 > 0 = 0 0 b) para ua proporcó H 0 H 1 Regó de rechazo p = p 0 p < p 0 p = p 0 p > p 0 p = p 0 p p 0 v) Pot crítcos de la dstrbucó ormal estadár P(Z 1,64) = 0,95 P(Z 1,96) = 0,975. 6

7 TABLAS DE LA DISTRIBUCIÓN NORMAL 7

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