A = c(4.21,4.13,4.24,4.32,4.18,4.10,4.18,4.28,4.23,4.27);
B = c(4.27,4.38,4.25,4.31,4.40,4.36,4.33,4.35,4.17,4.41);

n1 = length(A);
n2 = length(B);

mu1 = mean(A);
mu2 = mean(B);
 
s1 = sd(A);
s2 = sd(B);


sp2 = ((n1 - 1)*s1^2 + (n2 - 2)*s2^2)/(n1 + n2 - 2)
np = n1 + n2 - 2

# inverse CDF values for student t-distribution
t90 = qt(1-0.05,df=np);
t99 = qt(1-0.005,df=np);

# conf intervals
E90 = t90*sqrt(sp2*(1/n1 + 1/n2));
E99 = t99*sqrt(sp2*(1/n1 + 1/n2));

CI90 = c((mu1 - mu2) - E90, (mu1 - mu2) + E90)

CI99 =  c((mu1 - mu2) - E99, (mu1 - mu2) + E99)

print("90 % CI using T-distribution:\n")
print(CI90)

print("99 % CI using T-distribution:\n")
print(CI99)

# inverse std normal CDF values
z90 = qnorm(1-0.05)
z99 = qnorm(1-0.005)
E90n = z90*sqrt(s1^2/n1 + s2^2/n2)
E99n = z99*sqrt(s1^2/n1 + s2^2/n2)

CI90z = c((mu1 - mu2) - E90n, (mu1 - mu2) + E90n)
CI99z = c((mu1 - mu2) - E99n, (mu1 - mu2) + E99n)

print("90 % CI using normal distribution:\n")
print(CI90z)

print("99 % CI using normal distribution:\n")
print(CI99z)