#!/usr/bin/env python
# coding: utf-8

# In[2]:


import numpy as np
import matplotlib.pyplot as plt
import matplotlib.mlab as mlab
import scipy.stats as stats
import math
get_ipython().run_line_magic('matplotlib', 'inline')


# In[14]:


amostra = np.array([3, 2, 2, 2, 1, 2, 2, 2, 2, 3, 1, 2, 1, 2, 2, 0, 1, 2, 2, 1, 2, 1, 1,
       2, 2, 3, 2, 1, 2, 3, 4, 1, 1, 2, 1, 1, 1, 2, 3, 0, 2, 2, 1, 2, 3, 3,
       2, 2, 3, 2])


# In[15]:


amostra


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print('Média:',amostra.mean())
print('Desvio amostral:',amostra.std(ddof=1))


# In[34]:


print('z-score',stats.norm.ppf(.95))


# In[23]:


# Plot área 0,025 ou zscore 1,645


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mu = 0
variance = 1
sigma = math.sqrt(variance)
x = np.linspace(mu - 3*sigma, mu + 3*sigma, 100)
plt.plot(x,mlab.normpdf(x, mu, sigma))
y = mlab.normpdf(x,mu,sigma)
zc1 = mlab.normpdf(-1.645,0,sigma)
zc2 = mlab.normpdf(1.645,0,sigma)
plt.plot([0,0],[0,0.4])
plt.plot([-1.645,-1.645],[0,zc1],'r-')
plt.plot([1.645,1.645],[0,zc2],'b-')

plt.show()


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# Agora T de Student
nova = np.array([2, 1, 1, 3, 0, 1, 2, 1, 1, 2, 2, 0])
nova


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print('Média:',nova.mean(),'Desvio amostral:',nova.std(ddof=1))


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print('t-score',stats.t.ppf(0.05/2, 11))


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print(abs(stats.t.ppf(0.05/2, df=11)))


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plt.figure()
xs = np.linspace(-5,5,1000)
plt.plot(xs, stats.t.pdf(xs,11), 'k')
tc = abs(stats.t.ppf(0.05/2, df=11))
tc1 = stats.t.pdf(-tc,df=11)
tc2 = stats.t.pdf(tc,df=11)
tm = stats.t.pdf(0.0,df=11)
plt.plot([0,0],[0,tm])
plt.plot([-tc,-tc],[0,tc1],'r-')
plt.plot([tc,tc],[0,tc2],'b-')

plt.show()


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stats.t.ppf(0.05/2, df=11)


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# Qui-quadrado


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#x = np.linspace(0, 5, 50)
#plt.plot(x, stats.chi2.pdf(x, 49))


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# Xc esquerdo:
xesquerdo = (1 + 0.95) / 2
print('X esq',xesquerdo)

# Xc direito:
xdireito = (1 - 0.95) / 2
print('X dir',xdireito)

# Valor da probabilidade esquerda (df = graus de liberdade):
vpe = stats.chi2.isf(q=xesquerdo, df=49)
print('Val Prob Esq', vpe)

# Valor da probabilidade direita:
vpd = stats.chi2.isf(q=xdireito, df=49)
print('Val Prob Dir', vpd)

# Desvio padrão da amostra:
dp = amostra.std(ddof=1)
print('Desvio',dp)

# Limite inferior (esquerdo):
me = math.sqrt((49 * dp**2)/vpd)
print('Limite Esq',me)

# Limite superior (direito):
md = math.sqrt((49 * dp**2)/vpe)
print('Limite Dir',md)

# Testando: 
if dp <= md and dp >= me:
    print('Desvio válido')


# ## Amostras de queijo

# In[9]:


lote = np.array([58.5, 60.1, 60.02, 57.4, 60.3, 55.4, 58.2, 59.8, 54.3, 60.4, 60.7, 60.1, 55.6, 57.1, 60.0, 
                 60.7, 60.3, 56.7,  57.9, 59.01])


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print(len(lote))


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print('Média',lote.mean(),'Desvio',lote.std(ddof=1))


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vc = abs(stats.t.ppf(0.05, df=19))
print('valor crítico',vc)


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df = 19 # graus de liberdade
plt.figure()
xs = np.linspace(-5,5,1000)
plt.plot(xs, stats.t.pdf(xs,df), 'k')
tc = abs(stats.t.ppf(0.05, df=df))
tc1 = stats.t.pdf(-tc,df=df)
tm = stats.t.pdf(0.0,df=df)
plt.plot([0,0],[0,tm])
plt.plot([-tc,-tc],[0,tc1],'r-')

plt.show()


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t_score = (58.66 - 60) / (1.92 / math.sqrt(20))
print('t_score',t_score)
p_value = stats.t.sf(np.abs(t_score), 19) # precisamos passar o valor absoluto
print('p_value',p_value)


# In[24]:


df = 19 # graus de liberdade
plt.figure()
xs = np.linspace(-5,5,1000)
plt.plot(xs, stats.t.pdf(xs,df), 'k')
plt.show


# In[6]:


# Teste bicaudal
amostra = np.array([95.88,101.2,102.04,100.1,98.7,96.18,97.53,100.79,98.52,100.08,100.45,99.19,
                    99.91,101.01,98.78,101.02,98.78,100.18,100.94,97.12])


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mediah0 = 100 # média da Hipótese nula 100 mg
media = amostra.mean()
desvio = amostra.std(ddof=1)
n = len(amostra)
gl = n - 1
print('média',media,'desvio',desvio,'n',n,'gl',gl)


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alfa = 0.05
plt.figure()
xs = np.linspace(-5,5,1000)
plt.plot(xs, stats.t.pdf(xs,gl), 'k')
tc = abs(stats.t.ppf(0.05/2, df=gl))
print('T crítico 1',-tc,'T crítico 2',tc)
tc1 = stats.t.pdf(-tc,df=gl)
tc2 = stats.t.pdf(tc,df=gl)
print('tc1',tc1, 'tc2',tc2)
tm = stats.t.pdf(0.0,df=gl)
plt.plot([0,0],[0,tm])
plt.plot([-tc,-tc],[0,tc1],'r-')
plt.plot([tc,tc],[0,tc2],'b-')
t_observado = (media - mediah0) / (desvio / math.sqrt(n))
print('t_observado',t_observado)
a1 = stats.t.pdf(t_observado,df=gl)
a2 = a1 = stats.t.pdf(-t_observado,df=gl)
print('a1',a1,'a2',a2)
plt.plot([-t_observado,-t_observado],[0,a1],'k:')
plt.plot([t_observado,t_observado],[0,a2],'k:')
if t_observado > (-tc) and t_observado < tc:
    print('Não rejeitamos a hipótese nula')
else:
    print('Rejeitamos a hipótese nula')
print('alfa',alfa)
valor_p = stats.t.sf(np.abs(t_observado), n-1)*2
print('valor_p',valor_p)
if valor_p <= alfa:
    print('Rejeitamos a hipótese nula com base no valor_p')
else:
    print('Não rejeitamos a hipótese nula com base no valor_p')

plt.show()


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