import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
%config InlineBackend.figure_format = 'retina'
mean = np.mean(100)
std = np.sqrt(100)/2
# -1.96 < ( (x-mean)/std ) < 1.96
def comparefunx(x,mean,std):
if ( ((x-mean)/std ) < 1.96 and (( x-mean)/std ) > (-1.96)):
print("accept the hypothesis,%d is in confidence interval" %x)
return x
else:
print("abondan the hypothesis!")
n = comparefunx(100,mean,std)
accept the hypothesis,100 is in confidence interval
# 2
#总体均值为μ, 总体标准差为σ, 从中观测的n个数据x的样本均值X分布也是正态分布。X的分布平均值
#扔为a,标准差为σ/sqrt(n)（极简统计学P131）
# -1.96 < ( (x-mean)/(σ/sqrt(n)) ) < 1.96 95%置信区间
# -2.58 < ( (x-mean)/(σ/sqrt(n)) ) < 2.58 99%置信区间
def rangefunx(mean,std,n,range,interval):
low = mean - range * std / np.sqrt(n)
high = mean + range * std / np.sqrt(n)
print("%d percent confidence interval is : from %d to %d" %(interval,low,high))
return low,high
low,high = rangefunx(1082,108,30,1.96,95)
low1,high1 = rangefunx(1082,108,30,2.58,99)
95 percent confidence interval is : from 1043 to 1120
99 percent confidence interval is : from 1031 to 1132
