#import pandas as pd
import numpy as np
import scipy.stats as stats
#from scipy.stats import norm
#from scipy.stats import t
from scipy.stats.distributions import t as tdist

small = [41, 45, 42, 62, 68, 54, 52, 55, 44, 60]
large = [74,74,70,52,76,91,71,78,76,78,83,50,52,66,65,53,72]

print("Data Frame of small is : ",f'\n{small}\n')
print("Data Frame of large is : ",f'\n{small}\n')

s_mean = np.mean(small)
l_mean = np.mean(large)
print("Mean of small is : ",s_mean)
print("Mean of large is : ",l_mean)

s_var = np.var(small, ddof=1)
l_var = np.var(large, ddof=1)
print("Variance of small is : ",s_var)
print("Variance of large is : ",l_var)

s_p = np.sqrt((9*s_var+16*l_var)/25)
print("Standard deviation of pooled variance is : ",s_p)

t_cal = (s_mean-l_mean)/(s_p*(np.sqrt((1/10)+(1/17))))  
t_cal
print("Calculated Value of t Statistic is : ",t_cal)


res = stats.ttest_ind(a=small, b=large, equal_var=True, alternative='two-sided')
print(res)

t25 = tdist.ppf(0.025, df=25)
t25
print("Critical value of t distribution w/ p=0.05 and df=25 is : ",t25)