Explain what is meant by a margin of error for a confidence interval.
The conclusions of surveys are typically drawn from the population samples. The sample representation of the population is essential, and it usually is being determined by the two most important statistics. These are the margin of error and the confidence interval. The confidence interval and the margin of error measure how well the sample represents the entire population.
The margin of error is the precision that is required in a survey. For instance, a 5% margin of an error means that the variance of the actual findings could be negative or positive five points. If a survey has a 3% margin of error at a 95% level of confidence, this will mean that the data from the survey or the experiment would be 3 points above or below the percentage level of the confidence interval.
From the example, it can be deduced that the confidence interval and the margin of error describes a range of scores defining the plausible confines of a particular aggregate measure statistically. Frequently, the conclusions drawn from the sample surveys are being reported as having an accurate measure of a positive or negative percentage margin of error (+ – 3% ME). The confidence interval expresses these results more differently, that is within a particular range. Most importantly, both the margin of error and the confidence interval base their measures within a particular range. The range is within which the results will certainly fall. Therefore when two measures are significantly different, then the two ranges of probable results do not partly cover each other.
The margin of error is calculated by multiplying the standard error with the Z-score of the probable error to be accepted. The standard error which is symbolized by SE is gotten by dividing the square root of the variance, also known as the standard deviation (SD) of the population sample by the square root of the entire sum of statistical points that are drawn on (N). That is SE = SD/√N. This is a fairly easy way of getting the margin of error since the probabilities used are quite few and commonly used.
With an assumption of a particular level of confidence, size of the population and that the population is larger than the sample, the margin of error decreases as the sample size increases. This means that the small samples normally have a larger percentage of the margin of errors. Therefore the small samples in most cases do not accurately represent the population. As the sample size increases, the accuracy of the population representation increases; hence larger samples better represent the population than the smaller samples. Taking the 95% level of confidence and using the calculation above, the 3 percent margin of error would require a sample size of about 1000 units.
The margin of error and the confidence interval are normally being calculated for the total population. However, they should also be used to measure the precision of the sample subgroups in situations where the subgroups of a sample population are being considered. Generally, the margin of error indicates the inherent precisions in survey data. In most cases, the survey data represent a range and not a specific number.
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Custom-Writing.org. "Explain what is meant by a margin of error for a confidence interval." May 6, 2020. https://custom-writing.org/qna/explain-what-is-meant-by-a-margin-of-error-for-a-confidence-interval/.
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