ExamFI1_C1415. Lídia Montero. Thursday, January 15, 2015

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1 ExamFI1_C1415 Lídia Motero Thursday, Jauary 15, 015 Problem Descriptio: Budget Share of Food for Spaish Households is discussed. We have a cross-sectio dataset from 1980 ad 397 observatios related to households. Data is icluded i library Ecdat ad ca be loaded usig the data(budgetfood) commad. BudgetFood dataframe cotais: wfood percetage of total expediture which the household has spet o food totexp total expediture of the household age age of referece perso i the household size size of the household tow size of the tow where the household is placed categorised ito 5 groups: 1 for small tows, 5 for big oes sex sex of referece perso (ma,woma) Source: Delgado, A. ad Jua Mora (1998) Testig o ested semiparametric models : a applicatio to Egel curves specificatio, Joural of Applied Ecoometrics, 13(), I the ext questios a df subset without NA data ad 0 expediture i food is cosidered.a ew variable is defied cosistig o the total expediture i food per perso i household i euros, totfoodp. 1 #setwd("g:/lidia/mltm-mcaid/examens/curs1415/fi1exam") library(ecdat) library(car) library(effects) library(momets) data(budgetfood) ls() [1] "BudgetFood" "df" "ll" "m" "std" df<-budgetfood[!is.a(budgetfood$sex),] summary(df) wfood totexp age size Mi. :0.000 Mi. : Mi. :16.0 Mi. : st Qu.:0.58 1st Qu.: st Qu.:38.0 1st Qu.:.00 Media :0.364 Media : Media :50.0 Media : 4.00 Mea :0.378 Mea : Mea :50.5 Mea : rd Qu.: rd Qu.: rd Qu.:6.0 3rd Qu.: 5.00 Max. :0.997 Max. : Max. :99.0 Max. :17.00 tow sex Mi. :1.00 ma :064 1st Qu.:.00 woma: 3347 Media :4.00 Mea :3.4

2 3rd Qu.:4.00 Max. :5.00 df$totfoodp<-(df$totexp*df$wfood/df$size)/ ll<-which(df$totfoodp0);legth(ll) [1] 60 df<-df[-ll,] Descriptive results (umerical summaries ad graphical represetatios) are provided for the ew variable totfoodp. Let us discuss the distributio fittig for the target variable totfoodp. summary(df) wfood totexp age size Mi. : Mi. : 1616 Mi. :16.0 Mi. : 1.0 1st Qu.: st Qu.: st Qu.:38.0 1st Qu.:.0 Media : Media : Media :50.0 Media : 4.0 Mea : Mea : Mea :50.5 Mea : 3.7 3rd Qu.: rd Qu.: rd Qu.:61.0 3rd Qu.: 5.0 Max. : Max. : Max. :99.0 Max. :17.0 tow sex totfoodp Mi. :1.00 ma :0581 Mi. : 3 1st Qu.:.00 woma: st Qu.: 316 Media :4.00 Media : 49 Mea :3.4 Mea : 488 3rd Qu.:4.00 3rd Qu.: 589 Max. :5.00 Max. :5141 dim(df) [1] all.momets(df$totfoodp,order.max4, cetralt) [1] 1.000e+00.79e e e e+11 all.momets(df$totfoodp,order.max4) [1] 1.000e e e e e+11 Warig: package 'FAdist' was built uder R versio 3.1. [1] [1] 0.536

1. Calculate the upper threshold values i the euros per capita expediture i food that defie mild ad extreme outliers i some exploratory data aalysis tools as a boxplot. quatile((df$totfoodp),c(0.

3 1. Calculate the upper threshold values i the euros per capita expediture i food that defie mild ad extreme outliers i some exploratory data aalysis tools as a boxplot. quatile((df$totfoodp),c(0.75))+1.5*iqr((df$totfoodp)) 75% quatile((df$totfoodp),c(0.75))+3*iqr((df$totfoodp)) 75% Summary data for totfoodp target shows Q1 ad Q3 that allow to calculate the mild ad severe thresholds for outliers used commoly i boxplots: ad Calculate ad iterpret the skewess of totfoodp variable. The skewess of a radom variable X is defied as the third stadardized momet. It is usually deoted γ_1 ad correspods to the ratio of the third cetral momet, μ_3 ito the cubic power of the stadard deviatio e+07/(sd(df$totfoodp)^3) [1] skewess(df$totfoodp) [1] # With all.momets(,cetralt) data e+07/sqrt( e+04)^3 [1] Defie a list with o less tha 3 cadidate distributios that you cosider suitable for the target variable. Justify your criteria. Per cápita euro expediture i food is a o-discrete ad o-egative variable that accordig to the histogram is ot symmetric, i fact has positive skewess which meas to be log-right tailed. Cadidate distributios are loglogistic (blue), logormal (red), Weibull (orage),

4 Gamma ad Pareto. Goodess of fit is ot satisfactory to ay of them sice too extreme outliers are preset, but loglogistic distributio is the best cadidate i the list. Loglogistic distributio is kow i Ecoomy as Fisk distributio oe a trasformatio of the parametrizatio is performed. 4. A quick ad dirty procedure for distributio fittig produces some estimates for parameters ivolved i a Fisk distributio. The parameter alpha is a scale parameter ad is also the media of the distributio. The parameter beta is a shape parameter. The cumulative distributio fuctio ad the momets (ocetral, raw) are "E" [X_^k ]α^k (k π β)/sia(k π β) ad F(x)1/(1+(x/alpha)^(-beta)). Calculate theoretical momets ad compare to empirical momets (mea ad variace is eough, remember that the variace is the raw secod order momet mius the squared mea, i.e. V[X]E[X]- E[X]). library(fadist) library(mass) Attachig package: 'MASS' The followig object is masked from 'package:ecdat': SP500 fitdistr(df$totfoodp,"weibull") shape scale 1.856e e+0 (8.048e-03) (.036e+00) fitdistr(df$totfoodp,"logormal") mealog sdlog ( ) (0.0045) fitdistr(log(df$totfoodp),"logistic") locatio scale ( ) ( ) # Fisk parameters alpha is related to scale: exp( ) # beta is related to shape: 1/ alfaexp( ) beta 1/ # Theoretical mea for Fisk: alfa*(pi/beta)/si(pi/beta) # mea E[X] [1] ((alfa)^)*(*pi/beta)/si(*pi/beta) # E[X^] [1] ((alfa)^3)*(3*pi/beta)/si(3*pi/beta) # E[X^3] [1] (((alfa)^)*(*pi/beta)/si(*pi/beta))-((alfa*(pi/beta)/si(pi/beta))^ )# V[ X] E[X^]-E[X]^ [1] 9688 all.momets(df$totfoodp,order.max4, cetralf) [1] 1.000e e e e e+11 all.momets(df$totfoodp,order.max4, cetralt) [1] 1.000e+00.79e e e e+11 ks.test(log(df$totfoodp),"dlogis",scale ,locatio )

5 Warig: ties should ot be preset for the Kolmogorov-Smirov test Oe-sample Kolmogorov-Smirov test data: log(df$totfoodp) D , p-value <.e-16 alterative hypothesis: two-sided # Null hypothesis rejected, sample size is too large Raw momets ad Variace ca be computed usig provided data. First to third raw momets do ot differ so much,i higher order raw momets more discrepacies are foud. Theoretical variace is 89915, but empirical oe is 7946, so ot far away. Loglogistic/Fisk distributios seems coveiet to the target data. Let us discuss the target variable totfoodp meas accordig to the size of the residet tow ad/or the geder of the cotact perso. We select a radom sample of 1000 observatios i the subset of observatios without the upper extreme outliers (0.5% of the larger observatios firstly removed). wfood totexp age size Mi. : Mi. : 1616 Mi. :16.0 Mi. : 1.0 1st Qu.: st Qu.: st Qu.:38.0 1st Qu.:.0 Media : Media : Media :50.0 Media : 4.0 Mea : Mea : Mea :50.5 Mea : 3.7 3rd Qu.: rd Qu.: rd Qu.:61.0 3rd Qu.: 5.0 Max. : Max. : Max. :99.0 Max. :17.0 tow sex totfoodp Mi. :1.00 ma :0581 Mi. : 3 1st Qu.:.00 woma: st Qu.: 316 Media :4.00 Media : 49 Mea :3.4 Mea : 488 3rd Qu.:4.00 3rd Qu.: 589 Max. :5.00 Max. : Boxplot(dfs$totfoodp~dfs$tow,colraibow(5),id.0)

6 Boxplot(dfs$totfoodp~dfs$sex,colraibow(),id.0) 6 fliger.test(dfs$totfoodp~dfs$tow) Fliger-Killee test of homogeeity of variaces

7 data: dfs$totfoodp by dfs$tow Fliger-Killee:med chi-squared 5.446, df 4, p-value kruskal.test(dfs$totfoodp~dfs$tow) Kruskal-Wallis rak sum test data: dfs$totfoodp by dfs$tow Kruskal-Wallis chi-squared 10.79, df 4, p-value wilcox.test(dfs$totfoodp~dfs$sex,alterative"greater") Wilcoxo rak sum test with cotiuity correctio data: dfs$totfoodp by dfs$sex W 50443, p-value 1 alterative hypothesis: true locatio shift is greater tha 0 pairwise.wilcox.test(dfs$totfoodp,dfs$tow,alterative"less") Pairwise comparisos usig Wilcoxo rak sum test data: dfs$totfoodp ad dfs$tow P value adjustmet method: holm 7 cor(dfs[,c(7,1:5)],method"spearma") totfoodp wfood totexp age size tow totfoodp wfood totexp age size tow library(factomier) Warig: package 'FactoMieR' was built uder R versio codes(dfs,um.var7) $quati correlatio p.value wfood e-17 totexp e-06 age e-06 size e-30

8 $quali R p.value sex e-06 $category Estimate p.value woma e-06 ma e Is the average per capita expediture i food (Euros) equal for all tow sizes?. Does the average expediture icrease whe tow size icreases or ot? Idicate exceptios you fid ad justify your argumets Accordig to Kruskal-Wallis o-parametric Test for equal meas i the groups defied by tow size, p value is 3% less tha the 5% usual threshold, so evidece to reject the ull hypothesis is foud. Also, i the pairwise test output mea of the target i tow size i is always less tha the mea i tow size j oce i F) as.factor(tow) sex e-06 as.factor(tow):sex Residuals Sigif. codes: 0 '' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ``` summary(ma4) Call: lm(formula totfoodp ~ as.factor(tow) * sex, data dfs) Residuals: Mi 1Q Media 3Q Max Coefficiets: Estimate Std. Error t value Pr(> t ) (Itercept) <e-16 *** as.factor(tow) as.factor(tow) as.factor(tow) as.factor(tow) sexwoma as.factor(tow):sexwoma as.factor(tow)3:sexwoma as.factor(tow)4:sexwoma as.factor(tow)5:sexwoma Sigif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual stadard error: 41 o 990 degrees of freedom Multiple R-squared: 0.036, Adjusted R-squared: F-statistic: 3.71 o 9 ad 990 DF, p-value:

9 8. Which Two-Way Aova is cosistet with per capita expediture i food (Euros) data?. Justify your argumets Accordig to Aova(ma4) results iteractios betwee tow-size ad sex ad the mai towsize effect are ot sigificat. Thus a Oe-way aova model depedig o sex of the referece perso seems sigificace to explai average per capita food budget. 9. Iterpret the effect of sex i the Two-way Iteractive Aova model ma4 for the target variable The effect of a woma-referece HH o average per capita food budget i the smallest tow group is to icrease i 145. over the referece group (ma-referece). For tow size i group, the effect of woma-referece is (icreases average pc food budget i 13 compared to ma-referece HH). For tow size 3, beig a woma-referece HH decreases the target i 1 o average ( ). For tow size 4, beig a woma-referece HH (istead of ma-ref HH) icreases the target i aprox. Fially, i big cities, beig a woma-referece HH (istead of ma-ref HH) icreases the target i beig a woma-referece HH (istead of ma-ref HH) icreases the target i aprox. Coclusios are referred to the ma4 model, that does ot explai most of the variability of the target (explais 3%). So ot meaigful at all. Geeral liear models are to be cosidered for the ew target variable totexp, total expediture dim(dfs) [1] mm1<-lm(totexp~(i(100*wfood)+age+tow+poly(size,))*sex,datadfs) mm<-step(mm1,klog(1000)) 9 Start: AIC63 totexp ~ (I(100 * wfood) + age + tow + poly(size, )) * sex Df Sum of Sq RSS AIC - poly(size, ):sex 1.13e+1.6e tow:sex e+11.5e age:sex e+1.6e <oe>.5e I(100 * wfood):sex e+1.7e Step: AIC614 totexp ~ I(100 * wfood) + age + tow + poly(size, ) + sex + I(100 * wfood):sex + age:sex + tow:sex Df Sum of Sq RSS AIC - tow:sex e+10.6e age:sex e+1.7e <oe>.6e I(100 * wfood):sex e+1.8e poly(size, ) 4.49e+13.71e Step: AIC607 totexp ~ I(100 * wfood) + age + tow + poly(size, ) + sex +

10 I(100 * wfood):sex + age:sex Df Sum of Sq RSS AIC - age:sex e+1.7e <oe>.6e I(100 * wfood):sex 1.00e+1.8e tow 1.77e+1.9e poly(size, ) 4.5e+13.71e Step: AIC605 totexp ~ I(100 * wfood) + age + tow + poly(size, ) + sex + I(100 * wfood):sex Df Sum of Sq RSS AIC - age e+11.8e I(100 * wfood):sex e+1.9e <oe>.7e tow 1.87e+1.30e poly(size, ) 4.56e+13.73e Step: AIC600 totexp ~ I(100 * wfood) + tow + poly(size, ) + sex + I(100 * wfood):sex Df Sum of Sq RSS AIC - I(100 * wfood):sex e+1.9e <oe>.8e tow 1.74e+1.31e poly(size, ) 4.79e+13.76e Step: AIC6199 totexp ~ I(100 * wfood) + tow + poly(size, ) + sex Df Sum of Sq RSS AIC - sex e+10.9e <oe>.9e tow 1.96e+1.3e poly(size, ) 4.75e+13.77e I(100 * wfood) e e Step: AIC619 totexp ~ I(100 * wfood) + tow + poly(size, ) Df Sum of Sq RSS AIC <oe>.9e tow 1.91e+1.3e poly(size, ) 5.39e+13.83e I(100 * wfood) 1 7.7e e mm<-lm(totexp~(i(100*wfood)+tow+size+i(size^)),datadfs) summary(mm1) Call:

11 lm(formula totexp ~ (I(100 * wfood) + age + tow + poly(size, )) * sex, data dfs) Residuals: Mi 1Q Media 3Q Max Coefficiets: Estimate Std. Error t value Pr(> t ) (Itercept) <e-16 *** I(100 * wfood) <e-16 *** age * tow *** poly(size, ) <e-16 *** poly(size, ) sexwoma I(100 * wfood):sexwoma ** age:sexwoma * tow:sexwoma poly(size, )1:sexwoma * poly(size, ):sexwoma Sigif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual stadard error: o 988 degrees of freedom Multiple R-squared: 0.431, Adjusted R-squared: 0.45 F-statistic: 68.1 o 11 ad 988 DF, p-value: <e-16 summary(mm) 11 Call: lm(formula totexp ~ (I(100 * wfood) + tow + size + I(size^)), data dfs) Residuals: Mi 1Q Media 3Q Max Coefficiets: Estimate Std. Error t value Pr(> t ) (Itercept) < e-16 *** I(100 * wfood) < e-16 *** tow *** size e-11 *** I(size^) * --- Sigif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual stadard error: o 995 degrees of freedom Multiple R-squared: 0.41, Adjusted R-squared: F-statistic: 181 o 4 ad 995 DF, p-value: <e Write the equatios for the best geeral liear model that explais the total household expedidure. Idicate the coefficiet of determiatio for the model. Which is the average

12 expediture for a household i Barceloa havig as a referece perso a woma with 4 members o the mea for the rest of variables? coef(mm) (Itercept) I(100 * wfood) tow size I(size^) predict(mm,ewdatadata.frame(wfood ,tow5,size4)) total HH expediture i(100 wfood) tow size *size The model explais 4% of the variability of the total HH expediture. Accordig to the model mm: Barceloa is tow-size 5, the average wfood i % is 37.9 (see the summary at the begiig) ad family size is 4, the total HH expediture (i 1980 ptas, roughly 6000 ) Diagostics #iflueceidexplot(mm,id.7) iflueceplot(mm1,id.7) 1 StudRes Hat CookD

13 llc<-boxplot(cooks.distace(mm1),id.5,labelrow.ames(dfs)) 13 llr<-boxplot(rstudet(mm1),id.5,labelrow.ames(dfs))

11. Commet about the existece of large residuals. Which observatio has the largest leverage? Largest leverage belogs to 488, but lack of fit is ot preset.

14 11. Commet about the existece of large residuals. Which observatio has the largest leverage? Largest leverage belogs to 488, but lack of fit is ot preset. There are very large residuals i the positive part, this meas observed total HH expediture very, very large compared to model predictios (lack of fit). Observatio 1800 has a studet residual of 14!!!! Outliers i the total expediture are preset, the group of extremely rich people has to be cosidered separatelly. Assymetric structure i the residuals is detected Are there ifluece data i the selected sample? Idicate observatio idetifiers ad justify the aswer Ifluece data is related to Cook's distace, clearly observatios 1800, 1845 ad 7897 are ifluet data. The model is ot valid sice residuals are ot symmetric ad heterocedasticity might be preset. par(mfrowc(,)) plot(mm)

dfs[llc,] wfood totexp age size tow sex totfoodp 1800 0.03157 7974909 4 6 4 ma 5. 1854 0.1938 3476043 65 4 4 woma 1145.8 1445 0.351 389110 56 9 1 ma 838. 3308 0.06558 66898 67 5 woma 56.0 7897 0.

15 dfs[llc,] wfood totexp age size tow sex totfoodp ma woma ma woma ma Biary Respose: Let f.fo50 be a ew factor that idicates whether a household requests more tha 50% of its total expediture for food (high) or ot (low). This variable is the target variable. A table that relates the biary factor f.fo50 to the geder of the referece perso is icluded. dfs$f.fo50<-factor(ifelse(dfs$wfood<0.5,0,1),labelsc("low","high")) summary(dfs) wfood totexp age size Mi. : Mi. : 7176 Mi. :17.0 Mi. : st Qu.: st Qu.: st Qu.:39.0 1st Qu.:.00 Media : Media : Media :51.0 Media : 4.00 Mea : Mea : Mea :51.1 Mea : rd Qu.: rd Qu.: rd Qu.:63.0 3rd Qu.: 5.00 Max. : Max. : Max. :99.0 Max. :15.00 tow sex totfoodp f.fo50 Mi. :1.00 ma :846 Mi. : 5.9 low :777 1st Qu.:.00 woma:154 1st Qu.: 34.6 high:3 Media :4.00 Media : Mea :3.6 Mea : rd Qu.:4.00 3rd Qu.: Max. :5.00 Max. :178.0

16 xtabs(~sex+f.fo50,datadfs) f.fo50 sex low high ma woma 11 4 xtabs(~f.fo50,datadfs) f.fo50 low high m0<-glm(f.fo50~1,familybiomial,datadfs) m1<-glm(f.fo50~sex,familybiomial,datadfs) summary(m0) Call: glm(formula f.fo50 ~ 1, family biomial, data dfs) Deviace Residuals: Mi 1Q Media 3Q Max Coefficiets: Estimate Std. Error z value Pr(> z ) (Itercept) <e-16 *** --- Sigif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 (Dispersio parameter for biomial family take to be 1) Null deviace: o 999 degrees of freedom Residual deviace: o 999 degrees of freedom AIC: 1063 Number of Fisher Scorig iteratios: 4 16 summary(m1) Call: glm(formula f.fo50 ~ sex, family biomial, data dfs) Deviace Residuals: Mi 1Q Media 3Q Max Coefficiets: Estimate Std. Error z value Pr(> z ) (Itercept) <e-16 *** sexwoma Sigif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

17 (Dispersio parameter for biomial family take to be 1) Null deviace: o 999 degrees of freedom Residual deviace: o 998 degrees of freedom AIC: 1063 Number of Fisher Scorig iteratios: 4 aova(m0,m1,test"chisq") Aalysis of Deviace Table Model 1: f.fo50 ~ 1 Model : f.fo50 ~ sex Resid. Df Resid. Dev Df Deviace Pr(>Chi) Estimate a ull logit model (m0) statig that high food budget households do ot deped o the geder of the referece perso The costat is the atural logarithm of the odds of the margial probability of 'high food budget HH' (positive respoe), log(((181+4)/(665+11))) Estimate a logit model (m1) statig that high food budget households deped o the geder of the referece perso The costat is the atural logarithm of the odds of the probability of 'high food budget HH' (positive respoe) i the referece group (ma), log(((181)/(665))) The estimate for the dummy variable iterpreted as the additive effect o thelogit scale of beig a woma referece HH istead of ma (based level), the differece betwee the atural logarithm of the odds of the probability of 'high food budget HH' (positive respoe) i the referece group (ma), log(((181)/(665))) mius the atural logarithm of the odds of the probability of 'high food budget HH' (positive respose) i the alterative group (woma), log(((4)/(11))) ad this equals Iterpret the effect of the geder o the high food budget household i the logit, odds ad probability scales. Is geder of the referece perso a sigificat factor to explai the high food budget households Accordig to the Deviace test comparig models m0 ad m1, the ull hypothesis of equivalece betwee the models is accepted sice pvalue is greater tha the 5% usual threshold. Sex gross effect is ot sigificat. Beig a woma-hh istead of ma-hh icreased the logit of the probability of 'high food budget HH' (positive respose) by 0.3 uits Beig a woma-hh istead of ma-hh multiplies the odds of the probability of 'high food budget HH' (positive respose) by exp(0.3) Equivaletly, the odds are icreased 38%. Beig a woma-hh istead of ma-hh icreases the probability of 'high food budget HH' (positive respose) approximately by 0.3(1-0.33) uits.

18 Samplig Theory questios. Data icluded i the BudgetFood dataset is ot updated ad might be ot represetative for Catala households. We are iterested i the curret total household expediture ad probability of a high Budget i Food (more tha 50% of the total expediture). A radom sample without replacemet will be selected i the populatio of catala households. Accordig to IDESCAT the total umber of Catala households is i 011 ad i Barceloa urba area. Usig BudgetFood large dataset allows to obtai the variace of the household expediture i 01-Euro ^. Household expediture is estimated to be for household accordig to IDESCAT for 01 ad food budget is greater tha 50% of the total expediture i 14.6% of the households. vv<-((budgetfood$totexp)/ ) var(vv) [1] Calculate a 95% cofidece iterval for the average household expediture assumig a sample size 1000 households i Cataloia 95% Cofidece iterval for mea HH expediture: y z Vˆ µ [ y] y z Vˆ [ y] 0,995 Y + 0,995 y - z Vˆ [ y] µ y + z Vˆ [ ] Y y µ µ Y Y 18 ˆ y 1 S' N S' co z V ad where ( ) Determie the sample size to estimate the average household expediture i Cataloia for 015 with a absolute error less tha 3000 usig a cofidece level a0.05. Determie the sample size for the urba area of Barceloa EA 1 N [ y] z α V [ y] z α 1 S' z α S' β z 1 α S' β Cataloia N

19 ( + ) ( 1+ ) N ad for Barceloa N ( + ) ( 1+ ) N Determie the sample size to estimate the probability of eedig a Budget for Food that represets more tha 50% of the total household expediture i Cataloia for 015 with precisio of 5% usig a cofidece level a0.05. Repeat the sample size calculus for the urba area of Barceloa. 95% Cofidece iterval for a proportio: EA [ y] EA[ p] 1 pˆ ˆ z S' z z N N -1 ( 1 pˆ ) 0.146( ) 0 Sample size to esure the requested absolute precisio is: ( 0.146( ) ) Takig accout of populatio size, for Cataloia N ( + ) ( 1+ ) 1 N ad for Barceloa N ( + ) ( 1+ ) 1 N

Statistics for Economics & Business

Statistics for Economics & Business Statistics for Ecoomics & Busiess Cofidece Iterval Estimatio Learig Objectives I this chapter, you lear: To costruct ad iterpret cofidece iterval estimates for the mea ad the proportio How to determie