{"id":280866,"date":"2025-08-05T07:12:43","date_gmt":"2025-08-05T07:12:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=280866"},"modified":"2025-08-05T07:12:46","modified_gmt":"2025-08-05T07:12:46","slug":"in-a-recent-poll-200-people-were-asked-if-they-liked-dogs-and-37-said-they-did","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/05\/in-a-recent-poll-200-people-were-asked-if-they-liked-dogs-and-37-said-they-did\/","title":{"rendered":"\u00a0In a recent poll, 200 people were asked if they liked dogs, and 37% said they did"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/image-493.png\" alt=\"\" class=\"wp-image-280867\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is&nbsp;<strong>0.097<\/strong>.<\/p>\n\n\n\n<p>The margin of error is a statistic that expresses the amount of random sampling error in a survey\u2019s results. It quantifies the uncertainty of using a sample proportion to estimate the proportion for the entire population. To calculate the margin of error for a proportion, we use the following formula:<\/p>\n\n\n\n<p>Margin of Error (ME) = z* * \u221a[p\u0302(1-p\u0302) \/ n]<\/p>\n\n\n\n<p>In this formula:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>p\u0302\u00a0(p-hat) is the sample proportion.<\/li>\n\n\n\n<li>n\u00a0is the sample size.<\/li>\n\n\n\n<li>z*\u00a0is the critical value, which is determined by the confidence level.<\/li>\n<\/ul>\n\n\n\n<p>First, we identify the values from the problem. The sample size&nbsp;n&nbsp;is 100 people. The sample proportion&nbsp;p\u0302&nbsp;is 17%, which we write as the decimal 0.17.<\/p>\n\n\n\n<p>Next, we need to find the critical value&nbsp;z*&nbsp;for a 99% confidence level. A 99% confidence level means that 99% of the distribution is centered around the mean, leaving 1% of the probability in the tails of the standard normal distribution. This 1% is split equally between the two tails, so there is 0.5% (or 0.005) in each tail. The z-score that corresponds to a cumulative probability of 0.995 (1 minus 0.005) is approximately 2.576. This is our&nbsp;z*&nbsp;value.<\/p>\n\n\n\n<p>Now, we can plug all the values into the formula:<\/p>\n\n\n\n<p>ME = 2.576 * \u221a[(0.17 * (1 &#8211; 0.17)) \/ 100]<\/p>\n\n\n\n<p>We calculate the part inside the square root first:<br>ME = 2.576 * \u221a[(0.17 * 0.83) \/ 100]<br>ME = 2.576 * \u221a[0.1411 \/ 100]<br>ME = 2.576 * \u221a[0.001411]<\/p>\n\n\n\n<p>Taking the square root gives:<br>ME \u2248 2.576 * 0.03756<\/p>\n\n\n\n<p>Finally, we perform the multiplication:<br>ME \u2248 0.09676<\/p>\n\n\n\n<p>The question asks for the answer to be rounded to three decimal places. Rounding 0.09676 gives us 0.097.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/learnexams-banner5-304.jpeg\" alt=\"\" class=\"wp-image-280868\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The correct answer is&nbsp;0.097. The margin of error is a statistic that expresses the amount of random sampling error in a survey\u2019s results. It quantifies the uncertainty of using a sample proportion to estimate the proportion for the entire population. To calculate the margin of error for a proportion, [&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 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-280866","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280866","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=280866"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280866\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=280866"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=280866"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=280866"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}