Estimating the population mean in srswr with minimum sample size and minimum relative mean square error

This paper is focused on the impact of minimum sample size with minimum relative standard error on the estimation of the population mean in simple random sampling when sampling is with replacement. The data used in this paper is the data of the population of Fish caught by marine recreational Fishermen by species Group and Year of Atlantic and Gulf coasts. To show the above impact Three applications where executed for this purpose. In application one a minimum sample size under SRSWR with minimum relative standard error (RSE) equal to a given values ϕ ( 0.30, 0.31 , 0.32 , 0.33 , 0.34 , 0.35 ) is calculated, it has been shown that with every increases in the value of ϕ there is a significance decreases equal to one unit approximately in sample size, a 95% confidence interval for the population mean of fish is estimated as(2042.15 ,9416.13 ), An estimate of total number of fish is 395310.66. In application tow a sample of size n=15units is required to attain 35% relative standard error of the estimator of population mean under SRSWR sampling. In application three we selected a SRSWR sample of fifteen units from the 1999 Washington, D. C population during 1995 in each of the species group selected in the sampleAn estimate of mean number of fish in each species group during 1995 is 5503.60, the sample variance is 55510243.11, and the estimate of the variance of the estimator y ̅ ̂ is equal to 3700682.87 A 95% confidence interval for the mean number of fish in each one of the species group caught during 1995 in the hole country is [1377.23, 9629.97], from the confidence interval ranges the estimated mean value is significant.