# Variable declaration
n = 10 # Sample size
N = 1000 # population size
# Calculation
from scipy import *
from pylab import *
# as we know correction factor = (N-n)/(N-1)
corr_fact = (float(N-n))/(N-1) # correction factor
corr_fact = round(corr_fact,3)
# Result
print "Correction Factor: ",corr_fact
# Variable declaration
Mean = 513.3 # Mean( in square feet)
std_dev = 31.5 # Standard deviation ( in square feet)
n = 40 # Number of cans
x1 = 510.0 # lower limit of area (in square feet)
x2 = 520.0 # upper limit of area (in square feet)
# Calculation
from scipy import *
from pylab import *
# as we know Z = (X-Mean) / (std_dev/sqrt(n))
Z1 = round( ((x1-Mean) / (std_dev/sqrt(n))),3) # Z value corresponding to lower limit
Z2 = round( ((x2-Mean) / (std_dev/sqrt(n))),3) # Z value corresponding to upper limit
# Using values of Z1 & Z2 from Table-3
P = 0.6553 # Requires probability (from Table-3)
# Result
print "required probability: ",P
# Variable declaration
Mean = 12.40 # Mean( in minutes)
std_dev = 2.48 # Standard deviation ( in minutes)
n = 20 # sample size
x = 10.63 # observes time( in minutes)
# Calculation
from scipy import *
from pylab import *
t = (x-Mean) / (std_dev/sqrt(n)) # t-value corresponding to observation
t = round( t,2)
v = n-1 # degree of freedom
# corresponding to v = 19 , porbability that t will be below -2.861, is 0.005 (Table-4)
# As 0.005 is very small probability, so data tend to refute manufacturer's claim
# Result
print " The Data tend to refute manufacturer's claim"
# Variable declaration
n = 20 # sample size
var_pop = 0.000126 # variance of population
var_samp = 0.0002 # variance of sample
# Calculation
from scipy import *
from pylab import *
chi_square = ((n-1)*var_samp) / var_pop # chi square value
chi_square = round(chi_square , 1) # i.e. 30.2
# From Table-5 for v = 19 and alpha = 0.05, chi_square(thoeritical) = 30.1, thus probability will be less than 0.05
# Result
print "chi square value: ",chi_square
print "probability of rejection of shipment is less than 0.05"
# Variable declaration
n1 = 7 # Smaple-1 size
n2 = 13 # Smaple-2 size
# Calculation
from scipy import *
from pylab import *
# Using Table-6, for v1 = 6 and v2 = 12 ,F(0.05) = 3.00 thus probability is 0.05
P = 0.05 # required probability
# Result
print "required probability: ",P
# Variable declaration
v1 = 10 # Degree of freedom a corresponding to (a,b)
v2 = 20 # Degree of freedom b corresponding to (a,b)
# Calculation
from scipy import *
from pylab import *
# we need to find f(0.95) at (10,20) i.e. 1/ f(0.05) at(20,10)
f = 1 / 2.77 # Required value f(0.05) at(20,10) = 2.77 from Table-6
f = round(f,2)
# Result
print "F value: ",f