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

data = pd.read_excel("http://kanggc.iptime.org/book/data/chap11-3-2.xlsx")
data

var1 = data['var1']
var2 = data['var2']

d = var1 - var2

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

d_mean = np.mean(d)
d_mean
d_var = np.var(d, ddof=1)
d_var

t_cal = d_mean/(np.sqrt(d_var/6))
t_cal

t5_1 = tdist.ppf(0.05, df=5)
t5_1
t5_2 = tdist.ppf(0.95, df=5)
t5_2

print("Mean of d is : ",d_mean)
print("Variance of d is : ", d_var)
print("Calculated t-statistic is : ",t_cal)

res = stats.ttest_1samp(d, popmean=0, alternative='less')
print(res)

ci = res.confidence_interval(confidence_level=0.95)
print(ci)

ci.low
ci.high
print("The Lower Value of 95% Confidence Interval is :", ci.low)
print("The Upper Value of 95% Confidence Interval is :", ci.high)

print("Critical value of t distribution w/ p=0.05 and df=5 is : ",t5_1)