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A continuación continuación se muestran muestran las ventas ventas de cuatro cuatro tipos de baterías baterías diferentes diferentes a lo largo largo d Compruebe si si existe alguna alguna diferencia diferencia en las ventas ventas medias entre entre los diferentes tipos d VE! VE !A" A" "E "E#$ #$ E E !&' !&' *A! *A!// -// // -// 0// -// 0// -// 0// // -// 0// 0// 0// -// // a1 Elaborar el planteamiento de la 2ipótesis nula 3 la 2ipóte b1 +eali4ar el an5lisis de los resultados. An5lisis de varian4a de un factor +E"6E Grupos
Cuenta
Suma
*A! *A!*A!9 *A!8
0 0 0 0
88// 9-// 8// 9-//
A:&"&" )E VA+&A;A Origen de las variaciones
Entre grupos )entro de los grupos !otal !otal
Suma de cuadrados
Grados de libertad
89897. -/07/
9 -0
--/-07.
9
ANALISIS El valor critico de f es mayor que f por lo tanto, se rechaza la H0 y se acepta eiste diferencia si!ni"cativa en las ventas entre las diferentes tipos de #at
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e un mes. e baterías, use una signicancia del 7%. ( )E *A *A!E+&A !E+&A *A!9 *A!8 -// // // -// 0// 0// 0// // sis alternativa.
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E!A" )E A" )E&?E+E!E" !&'(" )E *A!E+&A.
!A" E)&A" E!+E (" )&?E+E!E" !&'(" )E *A!E+&A
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1" #l n$%ero n$%ero de bacterias bacterias por unidad de volu%en& volu%en& present presentes es en una población población despu despu en la si(uiente tabla:
X: Nº de horas
0
1
Y: Nº de bacterias
12
19
Calcula: a) Las %edias desviaciones t*picas de las variables& n$%ero de horas n$%ero de b b) La covarian+a de la variable bidi%ensional" c) #l coe,iciente de correlación" d) La recta de re(resión de Y sobre X" e) La relación es directa o inversa por qu!
a) %edia &esviacion
horas
bacterias
-. -/.0
99.0
b) X: Nº de de horas Y: Nº de bacterias
'( N) de horas *( *( N) de #acterias +ormula ovarianza %$
-.=<<<<<<<7 9/. /.0999 099999 999 999
99=. 99=.8 87--7-----------
9/.099999999
c) X: Nº de de horas Y: Nº de bacterias
'( N) de horas *( *( N) de #acterias +ormula oef$de$correl
/.=7=9=<8
/.=7=9=<8
d-
EC6AC&( )E %A % A +EC!A +EC!A
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8/ 9/ -/ / /
/
-
eEs relacion directamente proporcional
9
8
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de un cierto n$%ero de horas& viene e'presado
2
-
.
5
22
-.
/.
2
0
acterias"
9 8 horas bacterias
9.999999999 +esumen Estadísticas de la regresión
Coeciente de corr Coeciente de det +D- austado Error típico (bservaciones
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<
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y !
= -98 8 <-
edio de los cuadra
=-8.-078-0< -0.7<=/87<-
F
lor crítico de F
<0.-0=<<0/7 /.//7//9
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6n estud estudio io de de la lass pro propieda piedades des de arma armadura durass cconec onectada tadass con con placa placass met5l met5licas icas p ig2 ig2tF tF#a #aug uge e et etal al Co Conn nnec ecto torr 'la 'late tesO sO,, ?or ?ores estt 'r 'roduc oducts ts M., M., =7 =7=G =G 9=F8 9=F881 81 dio dio las las sig sig @PlbQpulg1 de tramos de placa de 8, <, 0, / 3 - pulg. 8G
9/=.- 8/=. 9./ 9-<. 9<.0 98=.0 9/=.7 8/-. 987.- 9<./ 8/8. 99./ 980.= 90.7 9=-.8 9<<.- 9./ 97. 8/=.= 9<7.9 90-./ 98<.7 8-.= 8<.8 899. 8/.< 908.- 9<-.< 8/7.8 88.0 8=.= 8/.7 879.8 88.- 8<.0
H!ien H!iene e algIn algIn efecto efecto la vari variaci ación ón de de la longit longitud ud de de plac placas as en en la rigide rigide44 axial axial prom prom
8K 9/=.8/=. 9 9-<. 9<.0 98=.0 9/= 7
0K 9=-.8 9<<.9 97. 8/=.= 9<7.9 90-
/K 98<.7 8-.= 8<.8 899. 8/.< 908.9<- <
-K 8/7.8 88.0 8=.= 8/.7 879.8 88.8< 0
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ra soportar tec2os @Lodeling Moints ade Nit2 uientes observaciones observaciones de índice de rigide4 axial
edio verdaderaJ ?ormule 3 pruebe las 2ipótesis
H0.no H0.no eis eiste te difer diferenc encia ia si!n si!ni"c i"cati ativa va en la ri!i ri!idez dez aia aiall se! se! H1. eiste diferencia si!ni"cativa en la ri!idez aial se!/n rec ech hazamos la hipo pottesis nula y acept pta amos la hipotes esiis alte + 10, 10, es mayor mayor al valor valor citrico citrico + 2,34 2,34 y decimos decimos que eist eist en la ri!idez aial se!/n la lon!itud de las placas
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n la lon!itud de las placas la lon!itud de las placas nativa ya que el valor e diferencias si!ni"cativa
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T/ no existe diferencia sig T existe diferencia signi
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icativa en el control de parasitos segIn la dosis administrada