import scipy.stats as stats

import numpy as np

young $=[29,37,33,27,28,32,31,34,27,29]$

old $=[18,15,23,13,12,21]$

# Independent samples

print$("$Independent$")$

# Less than test

print$("$Less$-$than"$)$

# Point estimate

pt$\_$est $=$ np$.$mean$($young$)-$ np$.$mean$($old$)$

print$($round$($pt$\_$est, $4))$

# Standard error

std$\_$err $=$ np$.$sqrt$($np$.$var$($young$,$ ddof$=1)/$len$($young$)+$ np$.$var$($old$,$ ddof$=1)/$len$($old$))$

print$($round$($std$\_$err, $4))$

# Test statistic

test$\_$stat $=($np$.$mean$($young$)-$ np$.$mean$($old$))/$ std$\_$err

print$($round$($test$\_$stat, $4))$

# Degrees of freedom

df $=$ len$($young$)+$ len$($old$)-2$

print$($int$($df$))$

# Critical value

crit$\_$val $=$ stats.t$.$ppf$(0\mathrm{.}90,$ df$)$

print$($round$($crit$\_$val, $4))$

# Conclusion

print$("$Yes$")$

# Margin of error

moe $=$ std$\_$err $*$ crit$\_$val

print$($round$($moe$,4))$

# Lower confidence bound

lcb $=$ pt$\_$est $-$ moe

print$($lcb$)$

# Confidence interval check

print$("$Yes$")$

# Possible error

print$("$Type II$")$