## Cost- sampling decisons, Operation Research

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Cost- sampling decisons

σ x¯ =S/√n

Where is the  standard  error of he mean is the standard devaluation of  the population and n is the sample size. Here  the standard  error  of the mean is expressed in terms  of money i, e. ± Rs. 10. If the  standard  deviation is 100  the factor  for 95 percent  confidence is 1.96 of standard deviation. Thus  the actual size  of the  sample  would be

10/ 1.96 = 100/√n

√n = 196/10

N = 384

The total  cost of  the budget  been reduced from  Rs.8000 to Rs. 7680= ( 384x 20)

Another  alternative may be to  increase  the allowable error  from a lower  level to  higher level  provided  it does  not affect  the attitude  of the  respondents. For  example  if the  error is increased to  15, the sample  size will be

σ x¯ =s/√n

1.5/1.96= 100√n

√n= 196/ 15

N= 169

Thus  the total  budget  will be reduced from  Rs. 8000 to Rs. 3380= ( 196x 20)

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