{"id":237710,"date":"2025-06-17T13:35:27","date_gmt":"2025-06-17T13:35:27","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=237710"},"modified":"2025-06-17T13:35:29","modified_gmt":"2025-06-17T13:35:29","slug":"using-yamanes-formula-what-is-the-appropriate-sample-size-for-a-population-of-25000-with-a-precision-level-of-5","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/17\/using-yamanes-formula-what-is-the-appropriate-sample-size-for-a-population-of-25000-with-a-precision-level-of-5\/","title":{"rendered":"Using Yamane&#8217;s formula, what is the appropriate sample size for a population of 25,000 with a precision level of 5%"},"content":{"rendered":"\n<pre id=\"preorder-ask-header-text\" class=\"wp-block-preformatted\">Using Yamane's formula, what is the appropriate sample size for a population of 25,000 with a precision level of 5%?\\n63\\n345\\n394\\n4<\/pre>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To determine the appropriate sample size using <strong>Yamane\u2019s formula<\/strong>, we apply the following equation:n=N1+N(e)2n = \\frac{N}{1 + N(e)^2}n=1+N(e)2N\u200b<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>nnn = sample size<\/li>\n\n\n\n<li>NNN = population size<\/li>\n\n\n\n<li>eee = level of precision (expressed as a decimal)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Given:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>N=25,000N = 25,000N=25,000<\/li>\n\n\n\n<li>e=0.05e = 0.05e=0.05 (which corresponds to 5% precision)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-step calculation:<\/h3>\n\n\n\n<p>n=25,0001+25,000(0.05)2n = \\frac{25,000}{1 + 25,000(0.05)^2}n=1+25,000(0.05)225,000\u200bn=25,0001+25,000(0.0025)n = \\frac{25,000}{1 + 25,000(0.0025)}n=1+25,000(0.0025)25,000\u200bn=25,0001+62.5n = \\frac{25,000}{1 + 62.5}n=1+62.525,000\u200bn=25,00063.5n = \\frac{25,000}{63.5}n=63.525,000\u200bn\u2248393.7n \\approx 393.7n\u2248393.7<\/p>\n\n\n\n<p>Rounding to the nearest whole number, the <strong>sample size is approximately 394<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Correct Answer:<\/h3>\n\n\n\n<p><strong>394<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>Yamane\u2019s formula provides a simplified method to calculate a sample size that ensures sufficient precision for survey-based studies. The 5% precision level means that the margin of error is acceptable at \u00b15 percentage points. This level is commonly used in research where a moderate level of confidence is sufficient and full enumeration is not feasible.<\/p>\n\n\n\n<p>In this case, applying the formula to a population of 25,000 results in a sample of about 394 respondents. This sample size strikes a balance between manageability and statistical reliability. It ensures that findings from the sample can be generalized to the entire population with a reasonable degree of accuracy. Among the provided options \u2014 63, 345, 394, and 4 \u2014 the correct and most appropriate answer is <strong>394<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-905.jpeg\" alt=\"\" class=\"wp-image-237711\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Using Yamane&#8217;s formula, what is the appropriate sample size for a population of 25,000 with a precision level of 5%?\\n63\\n345\\n394\\n4 The Correct Answer and Explanation is: To determine the appropriate sample size using Yamane\u2019s formula, we apply the following equation:n=N1+N(e)2n = \\frac{N}{1 + N(e)^2}n=1+N(e)2N\u200b Where: Given: Step-by-step calculation: n=25,0001+25,000(0.05)2n = \\frac{25,000}{1 + 25,000(0.05)^2}n=1+25,000(0.05)225,000\u200bn=25,0001+25,000(0.0025)n = \\frac{25,000}{1 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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