Determining Sample Size for estimatingMeans

a.Acceptable Errors: There  may be several errors  in the  sample  size. The researcher  will have  to decide those  errors. Which may  be acceptable to  the executive.  For  example  if the  marketing executive desires to spends Rs.10,000 per month  on advertisement he may willingly spend   ± 10 % of the said expenditure. The deviation is decided on the basis of the  acceptable mean of  ten expenditure. A large size error would  be unacceptable. Therefore ten management will  have  to determine various  errors related to the sampling procedures. How many  errors  will be  acceptable  to management  are decided before planning  the sampling.

b.Confidence Level  :The  next  factor  influencing the   sample size  is deciding the confidence level. The larger the size of the sample the larger will be the confidence level of the  estimate. In case of a 100 percent sample of the population the confidence of the estimate will  be a 100 percent accurate. But  the study of all elements of the population will  too costly and impractical. Therefore  a smaller size  sample is selected for  calculating the estimate. In  practice the  management may decide on a 90 percent 95 percent  or 99 percent confidence level. Ac confidence level  of 95 percent  is desirable for all purposes.  The remaining  5 percent  risk  is acceptable.  Depending  on a 95  percent  confidence  level, the  size  of he sample may  be  determined. In  case of the  estimate  size of  sample  is decided by  the followings  formula.

                                                                                 x  = s/ √n

    Where  x is the  estimate  of the standard  error  of the  man  and S is the sample  standard deviation and is the size of  he sample. We have  seen that ± 2  x as the  interval at 95.45 confidence level to  decide  a specific  estimate. If we  assume  that we  want  ± 10 % of the  estimate  the would  be :

But  in practice, the  standard  deviation of the  sample  is unknown  before  selection  of the  sample. If  is a  typical  case. The researcher tries  to known  from past  studies.