Sample size calculation Math Problem Example | Topics and Well Written Essays - 2250 words

Sample size calculation - Math Problem ExampleSampling is important in that we involve fewer respondents than using the entire population, the stress saves time and money and an appropriate have will represent the population in that the results derived from the sample will explain the population with less error. A gravid sample will waste time and money while a small sample will give inaccurate results.In any prone study if we were to determine the mean of the population and the mean of the sample there means are not the same, the difference between the two is termed as an error, then when determining the sample size we need to consider the expected error that will result to these differences. The other factor to consider is the margin of this error, this represents the maximum achievable difference between the sample mean and the population mean. We consider also consider the standard warp of the population, the reason why we consider the standard deviation is because we assu me that the population assumes a expression distribution which is depicted by the central limit theorem that states that as the number of variables increase indefinitely then the variables assumes a normal distribution.For a clustered study there is need to consider the sampling design when astute the sample size, we consider the number of clusters afterwards calculating the sample size, after determining the sample size as shown to a higher place we multiply the results by the number of clusters, the results of this are then mu... n = (1.96/2 . 6.9) /(0.4) 2n = 285.779In this case therefore we will use a sample size n =286 derived from rounding off the figure into the nearest exclusively number.Cluster samplingFor a clustered study there is need to consider the sampling design when calculating the sample size, we consider the number of clusters after calculating the sample size, after determining the sample size as shown above we multiply the results by the number of clusters, the results of this are then multiplied by the an expected non response or error, example use 5%. After multiplying we then divide the results by the number of clusters to determine the number of n in each cluster.Example assumes that we have 10 clusters and we assume the level of error is 5% from our above results the following will be the results285.779 X 10 = 2857.792857.79 X 1.05 = 3000.68We will consider a 3,000 sample size and for each cluster we will have n = 300Formula 2The other figure that can be used is where we have the prevalence of the variable being studies, in this case for example we have a prevalence rate of 40% of a disease and we use the following formulan = Z2. x (1-x)/ E2Where Z is the confidence interval where if we choose 95% the area under the normal curve will be 1.96E is the expected margin error and x is the expected prevalence of the variable being studied.Formula 3Cochran (1963) hypothesise a formula that could be used in the calculation of the sampl e size in a study, the formula is as followsn = (Z2 PQ)/ e2Where n is the sample size, Z is the confidence interval, P is the estimated proportion of the attribute under study, q is derived from 1 - p and finally e is the precision level.He further stated that the above sample would further be