#Z test means
z.test.pvalue<-function(xbar, mu, sigma, n, tails){
                                                  z=(xbar-mu)*sqrt(n)/sigma
                                                  if (z<0) {pv=pnorm(z, lower.tail = T)} else {pv=pnorm(z,lower.tail = F)}
                                                  z<-round(z,2)
                                                  v1<-c(z, pv)
                                                  v2<-c(z, 2*pv)
                                                  if(tails==1) {return(v1)}
                                                  if (tails==2) {return(v2)}
                                                  }
z.test.pvalue(9.5,10,0.8,20,2)

#Z test proportions
z.test.prop.pvalue<-function(x, n, p, tails){
                             z=(x/n - p)/sqrt(p*(1-p)/n)
                             if (z<0) {pv=pnorm(z, lower.tail = T)} else {pv=pnorm(z,lower.tail = F)}
                             z<-round(z, 2)
                             v1<-c(z, pv)
                             v2<-c(z, 2*pv)
                             if(tails==1) {return(v1)}
                             if(tails==2) {return(v2)}
}
# t test means
t.test.pvalue<-function(xbar, mu, s, n, tails){
                   t=(xbar-mu)*sqrt(n)/s
                   if (t<0) {pv=pt(t, n-1,lower.tail = T)} else {pv=pt(t, n-1,lower.tail = F)}
                   t<-round(t,2)
                   v1<-c(t, pv)
                   v2<-c(t, 2*pv)
                   if(tails==1) {return(v1)}
                   if (tails==2) {return(v2)}
}
t.test.pvalue(57,60,3.0,20,2)#example t test with summary

# 2 SAMPLES
#two proportions:
#prop.test(x=c(x1,x2), n=c(n1,n2), alternative="*", correct=F, conf.level= )
prop.test(x=c(38,23), n=c(85,90),alternative ="greater", correct=F ) # two porportions example

# two means t test:
install.packages("BSDA")
require(BSDA)
#tsum.test(mean1,s1,n1,mean2,s2,n2,alt="two.sided",conf.level=.95) # "two.sided", "less", "greater"
tsum.test(5.9,4.1,42,4.1,3.7,47, alt="greater",conf.level=.99) #exapmle two means t test with summary

# t.test(x, y , alternative = " * " mu =0,   paired = FALSE, var.equal = FALSE, conf.level = ) # where x and y are vectors of raw data.
x<-c(495,760,556,904,520,1005,743,660)# question 6 on Practice 9
y<-c(722,562,880,520,500,1250,750,1640,518,904,1150,805,480,970,605)
t.test(x, y , alternative ="less", mu =0, paired = FALSE, var.equal = FALSE)