# Q1 Sample Size Selection

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Assignment 2, Semester 2, 2017 (BUACC5931)

Q1 Sample Size Interviewing or collecting data from the entire population would result to accurate information since each element will have given their opinion unlike when they would have been represented by others. Considering that we had a population of 69,000 bank workers, taking the percentage pick at 50%, margin error of 0.05 and the confidence level at 95%, the accurate and correct number of bank workers that were supposed to be surveyed is 384. The expenses involved in collecting data from large sample size might involve covering a wider

## Q1 Sample Size Selection

Assignment 2, Semester 2, 2017 (BUACC5931)

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Q1 Sample SizeInterviewing or collecting data from the entire population would result to accurate information since each element will have given their opinion unlike when they would have been represented by others. The spread, expenses, time and all difficulties involved in surveying the entire population makes the researchers to prefer a sample. The quantity representing the proportion of the population is referred to as sample size. Coming up with suitable and correct size of the sample is vital in the collection of accurate information. For the collected information to be reliable, the sample size has to be correct and accurate. The sample size is calculated using the formula as follows;Sample size = P(1P)(0.051.96)2where P is percentage pick guess.The percentage guess can be a pick such as 40%, 50%, 60% etc. now, depending on which percentage pick has been made the size of the sample will vary. In most of the cases, 50% is normally preferred due to its bisection of the population and conservativism when determining the sample size. Considering that we had a population of 69,000 bank workers, taking the percentage pick at 50%, margin error of 0.05 and the confidence level at 95%, the accurate and correct number of bank workers that were supposed to be surveyed is 384. Choosing to survey 15,000 bank workers lead to working with large sample size since the number was far much above the recommended sample size of 384. Working with large sample sizes has advantages and disadvantages as they will be discussed.
Advantages and disadvantages of large sample size.It is advantageous working with large sample sizes since they help in minimizing marginal error. As a result, the outcomes’ accuracy of the ample are therefore improved. The statistic and point estimator confidence interval will tend to be in such a way that the population parameter is covered, this is according to (Clearly et al. 2014). The two research institutions that were incorporated to conduct the research being that they worked with the sample size of 15,000 bankers, it is therefore in our speculation that they must have obtained more accurate informationconcerning the subject in question as compared to when they would have worked with smaller sample size. Large sample size is also preferred because of their representativeness since most ofthe characteristics or elements in the population are covered including the outliers unlike small sample sizes (Belli et al. 2014).One of the disadvantages associated with large sample size is that it is more expensive. The expenses involved in collecting data from large sample size might involve covering a wider geographical area which will involve more cost unlike small sample size (Goodman et al. 2013). For instance, Union of Belgian Banks will incur much cost through the research institution in surveying 15,000 banker that were spread around the country. Additionally, working with large sample sizes is time consuming since a lot of time is involved to reach the individuals from various banks in various part of the country.1Factors considered when choosing a sample size1Cleary, M., Horsfall, J. and Hayter, M., “Statistic and point estimator confidence interval will tend to be in such a way that the population parameter is covered.” Data collection and sampling in qualitative research: does size matter?.(Journalof advanced nursing,2014), 70(3), pp.473-475.2Belly, S., Newman, A.B and Ellis, R.S., “Large sample size is preferred because of its representativeness since most of the characteristics or elements are covered including outliers unlike small sample size.” Velocity dispersion and dynamical masses for large sample galaxies, (The Astrophysical Journal, 2014), 783(2).3Goodman, J.K., Cryder, C.E. and Cheema, A., “Expenses involved in collecting data from large sample size might involve covering wider geographical area which will involve more cost unlike small sample size.” Data collection in flat world: The strengths and weaknesses of mechanical Turk samples. (Journal of Behavioral Decision Making, 2013). 26(3).
The prior information that is known by the researchers about the topic that is under study is one of the factors that should be considered when choosing sample size. This prior information mighthelp to make a decision on whether to increase or reduce the sample size since the estimators such as mean and variance can be used to carb the variation in the sample (Button et al. 2013). Another factor is the risk of values involved, that is, if the risk involved is to be high then small sample can be used but when the risk involved is to be low, then the sample size is to be made large to reduce the marginal error.2Q2 Sampling MethodsOut of the population of 69,000 bank workers, only 15,000 bankers were ought to be surveyed by the research institutions. The process of selecting members that will represent the groups fromthe population under study is referred to as sampling method. In this case therefore, the research institutions used stratified sampling method. This sampling method was preferred for used due tosome of the advantages it offers. One such advantages is that stratified sampling method reduces the sampling errors, this is according to (Ye et al. 2013). The population is divided into subgroups called strata where they are spread to ensure for representativeness of the population. Characteristics in the strata are selected by simple random sampling method in order to reduce oreliminate selection bias. The spread of strata and wide coverage by stratified sampling method ensures that the population of interest is highly and well represented in the selected sample.2Button Button, K.S., Ioannidis, J.P., Mokrysz, C., Nosek, B.A., Flint, J., Robinson, E.S. and Munafò, M.R., “Prior information might help to make a decision on whether to increase or reduce the sample size since estimators such as mean and variance can be used to carb variation in the sample.” Power failure: why small sample size undermines the reliability of neuroscience.(Nature Reviews Neuroscience, 2013), 14(5), pp.365-376.Ye, Y., Wu, Q., Huang, J.Z., Ng, M.K. and Li, X., “stratified sampling method reduces the sampling errors.” Stratified samplingfor feature subspace selection in random forests for high dimensional data. (Pattern Recognition,2013), 46(3), pp.769-787.

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