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

Sample size calculation - Math Problem Example Sampling is important in that we involve fewer respondents than using the entire population, the sample saves time and money and an appropriate sample will represent the population in that the results derived from the sample will explain the population with less error. A large sample will waste time and money while a small sample will give inaccurate results. In any given 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, therefore 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 possible difference between the sample mean and the population mean. We consider also consider the standard deviation of the population, the reason why we consider the standard deviation is because we assume that the population assumes a normal 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 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 mu... n = [(1.96/2 . 6.9) /(0.4)] 2 n = 285.779 In this case therefore we will use a sample size n =286 derived from rounding off the figure into the nearest whole number. Cluster sampling: For 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 results: 285.779 X 10 = 2857.79 2857.79 X 1.05 = 3000.68 We will consider a 3,000 sample size and for each cluster we will have n = 300 Formula 2: The other formula 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 formula: n = [Z2. x (1-x)]/ E2 Where Z is the confidence interval where if we choose 95% the area under the normal curve will be 1.96 E is the expected margin error and x is the expected prevalence of the variable being studied. Formula 3: Cochran (1963) formulated a formula that could be used in the calculation of the sample size in a study, the formula is as follows: n = (Z2 PQ)/ e2 Where 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

Business communication Essay Example | Topics and Well Written Essays - 750 words - 3

Business communication - Essay Example While writing, keep the key purpose in mind and by no means one should drift from it. Nonetheless, if during the way of writing, one notices that centre of attention has altered, it is imperative to correct writing as considered necessary to reveal the point with the intention of keeping an understandable, as well as logical document (Guffey, pp.27, 2007). The readers should be inform in the beginning how they will get advantage by reading the document; what they can achieve, which facts and figures can be found, or how they can be benefited from reading that document. Identifying the audience for which one is writing will assist in deciding the manner as well as substance of the document. If one is not certain regarding the readers then the writer should inquire from himself for whom he is writing the document as well as who is almost certainly get the advantage from his writing. If one is writing with the plan of advertising an artifact or service to a target market or supporting a cause, he might have to know the age of anticipated readers, the background of anticipated readers, the place where they live, their phase of life, their interests as well as activities, and what factors are important for them. These sorts of questions will assist the writer to aim his audience and then write for them (Locker & Kaczmarek, p.91, 2008). While one writes, he should take care of practical as well as other terminologies, short forms of words, in addition to abbreviations. Except that one is writing for a specially focused area, it is better to stay away from slang and to spell acronyms and abbreviations completely, at least when they are used first. Regardless of the readers, one usually does not have to be excessively conventional or reserved. A standard, relaxed tone will generally be helpful in getting the point across (Guffey, pp.13, 2007). As the reader has recognized, an effort should be made to foresee the facts that the reader would like or require,