{"id":191403,"date":"2025-02-15T06:16:34","date_gmt":"2025-02-15T06:16:34","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=191403"},"modified":"2025-02-15T06:16:36","modified_gmt":"2025-02-15T06:16:36","slug":"for-part-b-construct-90-and-95-confidence-intervals-for-the-population-proportion","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/15\/for-part-b-construct-90-and-95-confidence-intervals-for-the-population-proportion\/","title":{"rendered":"For part B, construct 90% and 95% confidence intervals for the population proportion"},"content":{"rendered":"\n<p>For part B, construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. b2. In a survey of 2241 U.S. adults in a recent year, 650 made a New Year&#8217;s resolution to eat healthier.\u00c3\u201a\u00c2<br>5B. For part B, construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals.<\/p>\n\n\n\n<p>b2. In a survey of 2241 U.S. adults in a recent year, 650 made a New Year&#8217;s resolution to eat healthier.\u00c3\u201a\u00c2<\/p>\n\n\n\n<p>5C. For part C, construct a 99% confidence interval for the population proportion. Interpret the results.\u00c3\u201a\u00c2<\/p>\n\n\n\n<p>c1. In a survey of 1000 U.S. adults, 700 think police officers should be required to wear body cameras while on duty.\u00c3\u201a\u00c2<\/p>\n\n\n\n<p>c2. In a survey of 600 United Kingdom teachers, 226 say they would wear a body camera in school.\u00c3\u201a\u00c2<\/p>\n\n\n\n<p>5d. You wish to estimate, with 95% confidence, the population proportion of U.S. adults who think congress is doing a good or excellent job. Your estimate must be accurate within 4% of the population proportion.\u00c3\u201a\u00c2<\/p>\n\n\n\n<p>d1. No preliminary estimate is available. Find the minimum sample size needed.\u00c3\u201a\u00c2<\/p>\n\n\n\n<p>d2. Find the minimum sample size needed, using a prior survey that found that 25% of U.S. adults think congress is doing a good or excellent job.\u00c3\u201a\u00c2<\/p>\n\n\n\n<p>dc. Compare the results from parts d1 and d2.\u00c3\u201a\u00c2<\/p>\n\n\n\n<p>5E. In a survey of 1000 U.S. adults, 490 oppose allowing transgender students to use the bathrooms of the opposite biological sex. Construct a 90% confidence interval for the population proportion of u&gt;s. adults who oppose allowing transgender students to use the bathrooms of the opposite biological sex.\u00c3\u201a\u00c2<\/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 confidence intervals and minimum sample size calculations are as follows:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Part B: Confidence Intervals for Population Proportions<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>90% Confidence Interval for b2<\/strong>: (0.274, 0.306)<\/li>\n\n\n\n<li><strong>95% Confidence Interval for b2<\/strong>: (0.271, 0.309) <strong>Interpretation<\/strong>: With 90% confidence, the true proportion of U.S. adults who made a resolution to eat healthier lies between 27.4% and 30.6%. With 95% confidence, this range is slightly wider, from 27.1% to 30.9%. The 95% confidence interval is broader because it represents a higher level of confidence.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Part C: Confidence Interval for Population Proportion<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>99% Confidence Interval for c1<\/strong>: (0.663, 0.737)<\/li>\n\n\n\n<li><strong>99% Confidence Interval for c2<\/strong>: (0.326, 0.428) <strong>Interpretation<\/strong>:<\/li>\n\n\n\n<li>For c1, with 99% confidence, the proportion of U.S. adults who think police officers should wear body cameras is between 66.3% and 73.7%.<\/li>\n\n\n\n<li>For c2, with 99% confidence, the proportion of UK teachers who would wear body cameras is between 32.6% and 42.8%. These intervals are wider due to the higher confidence level.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Part E: Confidence Interval<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>90% Confidence Interval for e<\/strong>: (0.464, 0.516) <strong>Interpretation<\/strong>: With 90% confidence, the true proportion of U.S. adults who oppose allowing transgender students to use bathrooms of the opposite biological sex is between 46.4% and 51.6%.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Part D: Minimum Sample Size Calculation<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Minimum Sample Size for d1<\/strong> (No preliminary estimate): 601<\/li>\n\n\n\n<li><strong>Minimum Sample Size for d2<\/strong> (Using prior estimate of 25%): 600 <strong>Interpretation<\/strong>: The sample size needed is approximately the same for both parts because using a prior estimate of 25% provides a less variable estimate than assuming no prior estimate.<\/li>\n<\/ul>\n\n\n\n<p>These results reflect how different levels of confidence (90%, 95%, 99%) influence the width of confidence intervals, with higher confidence intervals being wider to account for more certainty in the estimation.<\/p>\n\n\n\n<p>The table with these values is now displayed for you.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>For part B, construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. b2. In a survey of 2241 U.S. adults in a recent year, 650 made a New Year&#8217;s resolution to eat healthier.\u00c3\u201a\u00c25B. For part B, construct 90% and 95% confidence intervals for [&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-191403","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191403","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=191403"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191403\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=191403"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=191403"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=191403"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}