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(ANOVA un facteur) La cafine, ingre, est considre comme un stimulant. Le degr de stimulation et sa variabilit diffrent selon la dose absorbe. Afin d'analyser

(ANOVA  un facteur) La cafine, ingre, est considre comme un stimulant. Le degr de stimulation et sa variabilit diffrent selon la dose absorbe. Afin d'analyser l'effet de la cafine sur l'excution d'une tche physique, on a ralis l'exprience suivante. On a considr trois niveaux de traitement, 0, 100 et 200 milligrammes (mg) de cafine. Trente (30) tudiants ayant le mme ge et essentiellement de mme capacit physique ont t choisis et entrains  la dactylographie. Aprs la formation, dix (10)tudiants ont t rpartis alatoirement  chaque traitement. Ni le physiologiste ni les tudiants ne savaient  quel traitement tait assign chaque groupe (exprience en double aveugle). Seul le statisticien en tait au courant. Deux heures aprs l'administration du traitement, on a demand  chaque tudiant de taper des mots. Dans le tableau ci-aprs est prsent le nombre de mots taps par minute. EN: (one-way ANOVA) Caffeine, ingested, is considered a stimulating. The degree of stimulation and its variability differ according to the absorbed dose. In order to analyze the effect of caffeine on the performance of a physical task, the following experiment was carried out. Three treatment levels, 0, 100 and 200 milligrams (mg) of caffeine were considered. Thirty (30) students of the same age and essentially of the same physical ability were selected and trained in typing. After training, ten (10) students were randomly assigned to each treatment. Neither the physiologist nor the students knew which treatment each group was assigned to (double-blind experiment). Only the statistician knew about it. Two hours after the treatment was administered, each student was asked to type words. The table below shows the number of words typed per minute. Traitement, i Observations _____________________________________________________________________ i = 1, 0 mg Cafine 242, 245, 244, 248, 247, 248, 242, 244, 246, 242 (Placebo) _____________________________________________________________________ i = 2, 100 mg Cafine 248, 246, 245, 247, 248, 250, 247, 246, 243, 244 _________________________________________________________________ i = 3, 200 mg Cafine 246, 248, 250, 252, 248, 250, 246, 248, 245, 250 Consigne : cet exercice est  faire manuellement (montrez tous vos calculs). a) Formulez ce problme  l'aide d'un modle ANOVA  un facteur en dfinissant de faon prcise chacune des composantes de votre modle. b) Au seuil  = 5 %, testez l'hypothse de l'galit de l'effet des traitements. Formulez vos hypothses et votre rgle dcision. c) Avec un seuil de 5 %, testez l'hypothse individuelle que les traitements 1 et 2 ont la mme efficacit. d) En utilisant la mthode de Scheff, construisez un intervalle de confiance  95 % pour le contraste .

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