n1=75
n2=75
p1=10/100
p2=9/100
#two tailed test
#two sample test
#Z=(p1-p2)/sqrt(P*Q)*(1/n1+1/n2))
P=(n1*p1+n2*p2)/(n1+n2)
Q=1-P
Z=(p1-p2)/sqrt((P*Q)*(1/n1+1/n2))
Z
alpha=0.1
Z.alpha=qnorm(1-alpha)
Z.alpha 

xbar=9.5  #sample mean
muo=9.57   #population mean
sigma=0.4
n=180
z=(xbar-muo)/(sigma/sqrt(n))
z
alpha=0.05
z.alpha=qnorm(1-alpha)
z.alpha
#q3
n=30
xbar=112.5
muo=100
sigma=15
z=(xbar-muo)/(sigma/sqrt(n))
z
alpha=0.05
z.alpha=qnorm(1-alpha)
z.alpha
#Q.4
p1=18/200
p2=25/600
n1=200
n2=600
P=((n1*p1)+(n2*p2))/(n1+n2)
Q=1-P
z=(p1-p2)/sqrt((P*Q)*(1/n1+1/n2))
z
alpha=0.05
z.alpha=qnorm(1-alpha)
z.alpha

#Two mean test

a=c(175,168,168,190,156,181,182,175,174,179)
b=c(185,169,173,173,188,186,175,174,179,180)
n1=length(a)
n2=length(b)
z=abs((mean(a)-mean(b))/(sqrt(var(a)/n1 +var(b)/n2)))
z
pval=2*pnorm(z)
pval

#two sample test
x=c(117,90)
n=c(150,125)
prop.test(x,n,alternative="greater")
#two sample proportion test