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

data1 = pd.read_stata("http://kanggc.iptime.org/book/data/chap11-2-1.dta")
data1.head()

var1 = data1['var1']
var1.describe()

print("Data Frame of data1 is : ",f'\n{data1}\n')
print("Summary Statistics of data1 is : ", f'\n{data1.describe()}\n')

xbar = np.mean(var1)
xbar
xstd = np.std(var1, ddof=1)
xstd

#t14 = stats.t.ppf(0.95, 14)
#t14
t_cal = (xbar-34.5)/(xstd/np.sqrt(15))
t_cal

t14_1 = tdist.ppf(0.025, df=14)
t14_1
t14_2 = tdist.ppf(0.975, df=14)
t14_2

print("Mean of var1 is : ",f'\n{xbar}\n')
print("Standard Deviation of data1 is : ", f'\n{xstd}\n')
print("Calculated t-statistic is : ",f'\n{t_cal}\n')

res = stats.ttest_1samp(data1, popmean=34.5, alternative='two-sided')
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)