---

#15

n1=45
n2=38
s1=18
s2=15


gl2pob <- function(n1,n2,s1,s2){ 
  var1 <- s1^2
  var2 <- s2^2
  d1 <- var1/n1
  d2 <- var2/n2
  num <- (d1+d2)^2
  den <- d1^2/(n1-1)+d2^2/(n2-1)
  gl <- num/den
  gl
}

gradosl1=gl2pob(n1=45,n2=38,s1=18,s2=15)
gradosl1

## [1] 80.99003

OT1 = sqrt((18)^2/45+(15)^2/38)
T1 = qt(0.01,80,lower.tail = FALSE)

ME1= OT1*T
ME1

## [1] 3.622299

#valor p

Q=(60-51)/OT1
Q

## [1] 2.48461

pt(2.48,80,lower.tail = FALSE)

## [1] 0.007618962

NO RECHAZO

#16

n3=16
n4=12
s3=59.42
s4=51.74

OT2=sqrt((59.42)^2/16+(51.74)^2/12)
OT2

## [1] 21.06553

gl3pob <- function(n3,n4,s3,s4){ 
  var3 <- s3^2
  var4 <- s4^2
  d3 <- var3/n3
  d4 <- var4/n4
  num <- (d3+d4)^2
  den <- d3^2/(n3-1)+d4^2/(n4-1)
  gl <- num/den
  gl
}
gradosl1 = gl3pob(n3=16,n4=12,s3=59.42,s4=51.74)
gradosl1

## [1] 25.34144

T2 = qt(0.025,25,lower.tail = FALSE)                
ME2 = T2*OT2
ME2

## [1] 43.38528

VALOR P

(525-487)/OT2

## [1] 1.803895

pt(1.8,25,lower.tail = FALSE)

## [1] 0.04197043

RECHAZO

#17

n5=16
n6=10
s5=0.64
s6=0.75

gl4pob <- function(n5,n6,s5,s6){ 
  var5 <- s5^2
  var6 <- s6^2
  d5 <- var5/n5
  d6 <- var6/n6
  num <- (d5+d6)^2
  den <- d5^2/(n5-1)+d6^2/(n6-1)
  gl <- num/den
  gl
}
gradosl3=gl4pob(n5=16
                ,n6=10
                ,s5=0.64
                ,s6=0.75)

gradosl3

## [1] 16.9497

OT3=sqrt((0.64)^2/16+(0.75)^2/10)
OT3

## [1] 0.2860944

T3=qt(0.025,16,lower.tail = FALSE)

ME3=T3*OT3
ME3

## [1] 0.606493

#VALOR P

(6.82-6.25)/OT3

## [1] 1.992349

pt(1.99,16,lower.tail=FALSE)

## [1] 0.03198039

RECHAZO