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.