{"id":6197,"date":"2013-07-29T13:01:43","date_gmt":"2013-07-29T13:01:43","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6197"},"modified":"2014-12-02T08:26:59","modified_gmt":"2014-12-02T08:26:59","slug":"a-statistics-review-of-confidence-intervals","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2013\/07\/29\/a-statistics-review-of-confidence-intervals\/","title":{"rendered":"A Statistics Review of Confidence Intervals"},"content":{"rendered":"

Overview:\u00a0 What Is a Confidence Interval?<\/strong>
\nUnless the population is small enough to determine each member, researchers cannot know the exact value of the population mean.\u00a0 However, using statistical techniques, it can be predicted that the mean falls within a certain range, called the confidence interval.\u00a0 Using properties of sample size, standard deviation, and probability distributions, \u00a0it can be estimated.<\/p>\n

How Can an Estimate Be Found?<\/strong>
\nThe population is almost always large enough that the only way to measure it is to take a sample from it and estimate the probable values of the population mean \u00a0(represented by \u03bc) and the standard deviation (represented by \u03c3) by the sample mean (X) and the sample standard deviation (s).\u00a0 The values from one sample may not be close because of sampling error.\u00a0 However, in order to be confident that the true value of the population mean is somewhere within an estimate, statisticians use large enough samples to ensure that the range of possible values contains the value that is desired.<\/p>\n

Why Is Sample Size Important?<\/strong>
\nSample size is important for two reasons.\u00a0 First, the larger the sample, the more likely that a distribution of means from large samples will form a normal curve.\u00a0 Therefore, the mean, median, and mode of that distribution will be equal, the measure of area under the curve will follow the same parameters, and the curve will be continuous, with an infinite number of points \u00a0from which \u00a0to choose the population mean.\u00a0 Second, the larger the sample, the smaller the margin of error.\u00a0 This is because there are more data points from which to select.<\/p>\n

How Is the Confidence Interval Increased?<\/strong>
\nBesides increasing the size of the sample, the size of the confidence interval itself can be widened.\u00a0 An area represented by one standard deviation below the mean to one standard deviation above the mean will cover about 68 % of the total area.\u00a0 In other words, it can be predicted with 68% accuracy that the mean is somewhere in that area.\u00a0 In order to increase the prediction to 95%, the size of the confidence interval can be widened to between 1.96 standard deviation above and below the mean.<\/p>\n

How Can the Sample Be Affected?<\/strong>
\nIn order for the chosen sample to accurately represent the underlying population, it must be truly random.\u00a0 If the sample is chosen for convenience or selected in a way that reflects bias, the other statistical techniques\u00a0 won’t ensure meaning.\u00a0 In addition, if the sample is too small, outliers will have more effect on the overall findings.<\/p>\n

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Overview:\u00a0 What Is a Confidence Interval? Unless the population is small enough to determine each member, researchers cannot know the exact value of the population mean.\u00a0 However, using statistical techniques, it can be predicted that the mean falls within a certain range, called the confidence interval.\u00a0 Using properties of sample size, standard deviation, and probability […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2,17],"tags":[373,1202,1581],"class_list":["post-6197","post","type-post","status-publish","format-standard","hentry","category-algebra","category-statistics-2","tag-confidence-intervals","tag-normal-curve","tag-sample-size"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6197","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=6197"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6197\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6197"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6197"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6197"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}