{"id":1159,"date":"2021-03-15T00:53:23","date_gmt":"2021-03-15T00:53:23","guid":{"rendered":"https:\/\/alminawi.com\/?p=507"},"modified":"2025-09-27T13:01:16","modified_gmt":"2025-09-27T13:01:16","slug":"audit-sampling-episode-10-sample-size-formula-standard-classical-variable-sampling","status":"publish","type":"post","link":"https:\/\/e.americanpro.org\/?p=1159","title":{"rendered":"Audit Sampling: Episode 10, Sample Size Formula, Standard Classical Variable Sampling"},"content":{"rendered":"<p data-start=\"201\" data-end=\"556\">Determining an appropriate sample size is crucial in audit sampling to ensure results are statistically reliable and cost-effective. Key factors impacting sample size include population size, confidence level, variability (standard deviation), tolerable misstatement, and expected misstatement. One formula that explicitly incorporates population size is:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Sample Size=( (<span class=\"mord text\"><span class=\"mord\">Population Size\u00a0<\/span><\/span><span class=\"mbin\">\u00d7 <\/span><span class=\"mord text\"><span class=\"mord\">Confidence Coefficient\u00a0<\/span><\/span><span class=\"mbin\">\u00d7 <\/span><span class=\"mord text\"><span class=\"mord\">Standard Deviation)\/ (Tolerable\u00a0Misstatement<span class=\"mbin\">\u2212<\/span>Estimated\u00a0Misstatement) )2<\/span><\/span><\/span><\/span><\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-509\" src=\"https:\/\/americanpro.org\/wp-content\/uploads\/2025\/06\/Sample-Size-300x79.png\" alt=\"\" width=\"300\" height=\"79\" \/><\/p>\n<p data-start=\"642\" data-end=\"650\">Where:<\/p>\n<ul data-start=\"651\" data-end=\"840\">\n<li data-start=\"651\" data-end=\"678\">\n<p data-start=\"653\" data-end=\"678\"><span class=\"katex\"><span class=\"katex-mathml\">NN<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">N<\/span><\/span><\/span><\/span> = population size<\/p>\n<\/li>\n<li data-start=\"679\" data-end=\"723\">\n<p data-start=\"681\" data-end=\"723\"><span class=\"katex\"><span class=\"katex-mathml\">ZZ<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">Z<\/span><\/span><\/span><\/span> = confidence coefficient (Z-score)<\/p>\n<\/li>\n<li data-start=\"724\" data-end=\"769\">\n<p data-start=\"726\" data-end=\"769\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c3\\sigma<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">\u03c3<\/span><\/span><\/span><\/span> = estimated standard deviation<\/p>\n<\/li>\n<li data-start=\"770\" data-end=\"805\">\n<p data-start=\"772\" data-end=\"805\"><span class=\"katex\"><span class=\"katex-mathml\">TMTM<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">TM<\/span><\/span><\/span><\/span> = tolerable misstatement<\/p>\n<\/li>\n<li data-start=\"806\" data-end=\"840\">\n<p data-start=\"808\" data-end=\"840\"><span class=\"katex\"><span class=\"katex-mathml\">EMEM<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">EM<\/span><\/span><\/span><\/span> = expected misstatement<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"842\" data-end=\"1091\">For example, an auditor testing 10,000 accounts receivable uses a 90% confidence level (<span class=\"katex\"><span class=\"katex-mathml\">Z=1.64Z = 1.64<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">Z<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">1.64<\/span><\/span><\/span><\/span>) with an estimated standard deviation of $20. The tolerable misstatement is $40,000, and the expected misstatement is $15,000. Applying the formula:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-508\" src=\"https:\/\/americanpro.org\/wp-content\/uploads\/2025\/06\/Sample-Size-2-300x52.png\" alt=\"\" width=\"300\" height=\"52\" \/><\/p>\n<p data-start=\"1190\" data-end=\"1438\">This means the auditor should sample approximately 172 accounts. This larger sample size reflects the substantial population and relatively narrow margin between tolerable and expected misstatement, ensuring the audit provides sufficient assurance.<\/p>\n<p data-start=\"1440\" data-end=\"1668\">In summary, incorporating population size directly in the sample size formula can lead to more conservative sampling and better risk mitigation, though auditors must balance practicality and efficiency in final sample decisions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Determining an appropriate sample size is crucial in audit sampling to ensure results are statistically reliable and cost-effective. Key factors impacting sample size include population size, confidence level, variability (standard deviation), tolerable misstatement, and expected misstatement. One formula that explicitly incorporates population size is: Sample Size=( (Population Size\u00a0\u00d7 Confidence Coefficient\u00a0\u00d7 Standard Deviation)\/ (Tolerable\u00a0Misstatement\u2212Estimated\u00a0Misstatement) )2 Where: [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":1011,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[17],"tags":[],"class_list":["post-1159","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-internal-audit"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/e.americanpro.org\/wp-content\/uploads\/2021\/03\/3-e1750015916881.avif","_links":{"self":[{"href":"https:\/\/e.americanpro.org\/index.php?rest_route=\/wp\/v2\/posts\/1159","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/e.americanpro.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/e.americanpro.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/e.americanpro.org\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/e.americanpro.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1159"}],"version-history":[{"count":1,"href":"https:\/\/e.americanpro.org\/index.php?rest_route=\/wp\/v2\/posts\/1159\/revisions"}],"predecessor-version":[{"id":2143,"href":"https:\/\/e.americanpro.org\/index.php?rest_route=\/wp\/v2\/posts\/1159\/revisions\/2143"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/e.americanpro.org\/index.php?rest_route=\/wp\/v2\/media\/1011"}],"wp:attachment":[{"href":"https:\/\/e.americanpro.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1159"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/e.americanpro.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1159"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/e.americanpro.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1159"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}