{"id":197955,"date":"2025-03-07T19:58:05","date_gmt":"2025-03-07T19:58:05","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=197955"},"modified":"2025-03-07T19:58:07","modified_gmt":"2025-03-07T19:58:07","slug":"administrators-in-a-large-school-district-asked-a-random-sample-of-seventh-grade-girls-to-take-an-iq-test","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/07\/administrators-in-a-large-school-district-asked-a-random-sample-of-seventh-grade-girls-to-take-an-iq-test\/","title":{"rendered":"Administrators in a large school district asked a random sample of seventh-grade girls to take an IQ test"},"content":{"rendered":"\n<p> Administrators in a large school district asked a random sample of seventh-grade girls to take an IQ test. They calculated a 99% confidence interval for the mean IQ as (95.3, 109.2).<\/p>\n\n\n\n<p>Which of the following is a correct interpretation of this interval?<\/p>\n\n\n\n<p>&nbsp;(a) The mean IQ of all seventh-grade girls in the school district is between 95.3 and 109.2, with 99% confidence (b) Ninety-nine percent of the time, mean IQ\u00e4s of seventh-grade girls will belong to the interval (95.3, 109.2).<\/p>\n\n\n\n<p>(c) Ninety-nine percent of the IQ\u00e5s are between 95.3 and 109.2.<\/p>\n\n\n\n<p>(d) There is a 1% probability that the mean IQ of all seventh-grade girls is not in this confidence interval.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The correct answer is <strong>(a)<\/strong>: The mean IQ of all seventh-grade girls in the school district is between 95.3 and 109.2, with 99% confidence.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>A <strong>confidence interval<\/strong> provides a range of values that is likely to contain the true population parameter (in this case, the mean IQ) with a specified level of confidence. The interval that the administrators calculated is a <strong>99% confidence interval<\/strong>, which means that if they were to repeatedly take random samples of seventh-grade girls and compute confidence intervals for each sample, 99% of those intervals would contain the true mean IQ of all seventh-grade girls in the school district.<\/p>\n\n\n\n<p>Let&#8217;s break down the options:<\/p>\n\n\n\n<p><strong>(a) The mean IQ of all seventh-grade girls in the school district is between 95.3 and 109.2, with 99% confidence.<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>This is the correct interpretation of a confidence interval. The interval (95.3, 109.2) gives a range in which we are 99% confident that the true mean IQ of all seventh-grade girls in the district lies. It reflects the uncertainty about the population mean and the degree of confidence (99%) associated with the estimate.<\/li>\n<\/ul>\n\n\n\n<p><strong>(b) Ninety-nine percent of the time, mean IQs of seventh-grade girls will belong to the interval (95.3, 109.2).<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>This interpretation is incorrect. The confidence interval does not predict that individual IQ scores fall within this range. Instead, it pertains to the population mean IQ of all seventh-grade girls in the school district. The interval is about the <strong>mean<\/strong> of the population, not about individual data points.<\/li>\n<\/ul>\n\n\n\n<p><strong>(c) Ninety-nine percent of the IQs are between 95.3 and 109.2.<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>This is incorrect because it confuses individual IQ scores with the population mean. The confidence interval does not suggest that 99% of individual IQ scores fall between 95.3 and 109.2. It provides an estimate for the population mean IQ.<\/li>\n<\/ul>\n\n\n\n<p><strong>(d) There is a 1% probability that the mean IQ of all seventh-grade girls is not in this confidence interval.<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>This interpretation is also incorrect. The interval does not imply a probability for the true mean falling within the interval. The true population mean is either inside the interval or outside of it, and we can be 99% confident that it lies inside the interval. The 1% refers to the <strong>confidence level<\/strong>, not a probability of the mean being outside the interval.<\/li>\n<\/ul>\n\n\n\n<p>In summary, option <strong>(a)<\/strong> is the correct interpretation because it properly explains that the confidence interval estimates the range of the true population mean IQ with 99% confidence.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Administrators in a large school district asked a random sample of seventh-grade girls to take an IQ test. They calculated a 99% confidence interval for the mean IQ as (95.3, 109.2). Which of the following is a correct interpretation of this interval? &nbsp;(a) The mean IQ of all seventh-grade girls in the school district is [&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-197955","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/197955","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=197955"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/197955\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=197955"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=197955"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=197955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}