{"id":216059,"date":"2025-05-18T12:38:50","date_gmt":"2025-05-18T12:38:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=216059"},"modified":"2025-05-18T12:38:53","modified_gmt":"2025-05-18T12:38:53","slug":"which-of-the-following-is-not-a-commonly-used-practice","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/18\/which-of-the-following-is-not-a-commonly-used-practice\/","title":{"rendered":"Which of the following is not a commonly used practice"},"content":{"rendered":"\n

Which of the following is not a commonly used practice? Choose the correct answer below.<\/p>\n\n\n\n

A. If the original population is not normally distributed and n > 30, the distribution of the sample means can be approximated reasonably well by a normal distribution.
B. If the distribution of the sample means is normally distributed, and n > 30, then the population distribution is normally distributed.
C. If the original population is normally distributed, then for any sample size n, the sample means will be normally distributed.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct answer is:<\/p>\n\n\n\n

B. If the distribution of the sample means is normally distributed, and n > 30, then the population distribution is normally distributed.<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/strong><\/h3>\n\n\n\n

Understanding how sample means behave in relation to the population distribution is a fundamental concept in inferential statistics. Let\u2019s explore why option B<\/strong> is not<\/strong> a commonly used or valid statistical practice.<\/p>\n\n\n\n

\n\n\n\n

Central Limit Theorem (CLT):<\/strong><\/h4>\n\n\n\n

The Central Limit Theorem<\/strong> is a foundational statistical principle that states:<\/p>\n\n\n\n

\n

Regardless of the population distribution, the sampling distribution of the sample means approaches a normal distribution<\/strong> as the sample size (n<\/strong>) becomes large (typically n > 30<\/strong> is used as a rule of thumb).<\/p>\n<\/blockquote>\n\n\n\n

This means:<\/p>\n\n\n\n

    \n
  • If the population is not normally distributed<\/strong> but n > 30<\/strong>, we can still assume that the sampling distribution of the sample means<\/strong> is approximately normal. (This supports option A.<\/strong>)<\/li>\n\n\n\n
  • If the population is normally distributed<\/strong>, then the sampling distribution of the sample means<\/strong> will also be normally distributed even for small sample sizes<\/strong>. (This supports option C.<\/strong>)<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    Why Option B is Incorrect:<\/strong><\/h4>\n\n\n\n

    Option B<\/strong> tries to reverse<\/strong> the logic of the Central Limit Theorem. It suggests that if the sample means are normally distributed<\/strong>, then the population must also be normally distributed<\/strong>. This is not necessarily true<\/strong>.<\/p>\n\n\n\n

    \n\n\n\n

    Conclusion:<\/strong><\/h3>\n\n\n\n

    The correct answer is B<\/strong>, because it incorrectly infers properties of the population from the sampling distribution. Options A and C are based on established statistical principles and are widely accepted in practice.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Which of the following is not a commonly used practice? Choose the correct answer below. A. If the original population is not normally distributed and n > 30, the distribution of the sample means can be approximated reasonably well by a normal distribution.B. If the distribution of the sample means is normally distributed, and n […]<\/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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-216059","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/216059","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=216059"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/216059\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=216059"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=216059"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=216059"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}