{"id":210419,"date":"2025-04-30T09:19:48","date_gmt":"2025-04-30T09:19:48","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=210419"},"modified":"2025-04-30T09:19:49","modified_gmt":"2025-04-30T09:19:49","slug":"we-could-narrow-a-95-percent-confidence-interval-by","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/30\/we-could-narrow-a-95-percent-confidence-interval-by\/","title":{"rendered":"We could narrow a 95 percent confidence interval by"},"content":{"rendered":"\n

We could narrow a 95 percent confidence interval by:<\/p>\n\n\n\n

A. using 99 percent confidence.
B. using a larger sample.
C. raising the standard error.<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

Correct Answer: B. using a larger sample.<\/strong><\/p>\n\n\n\n

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

A 95% confidence interval (CI)<\/strong> is a statistical range used to estimate an unknown population parameter (such as a mean or proportion). It provides an interval of values that likely includes the true value, with 95% confidence. The width of the confidence interval depends primarily on three factors:<\/p>\n\n\n\n

    \n
  1. The confidence level<\/strong> (e.g., 95% or 99%)<\/li>\n\n\n\n
  2. The variability in the data<\/strong> (standard deviation or standard error)<\/li>\n\n\n\n
  3. The sample size<\/strong><\/li>\n<\/ol>\n\n\n\n

    To narrow a confidence interval<\/strong>, we want to reduce the margin of error. The margin of error (ME)<\/strong> in a confidence interval is calculated as:<\/p>\n\n\n\n

    [
    \\text{ME} = z \\times \\frac{\\sigma}{\\sqrt{n}}
    ]<\/p>\n\n\n\n

    Where:<\/p>\n\n\n\n

      \n
    • ( z ) is the z-score associated with the desired confidence level (e.g., 1.96 for 95%)<\/li>\n\n\n\n
    • ( \\sigma ) is the population standard deviation<\/li>\n\n\n\n
    • ( n ) is the sample size<\/li>\n<\/ul>\n\n\n\n

      Let’s examine the choices:<\/h4>\n\n\n\n

      A. Using 99 percent confidence<\/strong>
      This is incorrect. Increasing the confidence level from 95% to 99% actually widens<\/strong> the confidence interval. A higher confidence level requires a larger margin of error to ensure the interval captures the true population parameter more often.<\/p>\n\n\n\n

      B. Using a larger sample<\/strong>
      This is correct<\/strong>. Increasing the sample size ( n ) decreases the standard error (( \\frac{\\sigma}{\\sqrt{n}} )), which in turn narrows the confidence interval<\/strong>. Larger samples provide more precise estimates, reducing variability.<\/p>\n\n\n\n

      C. Raising the standard error<\/strong>
      This is incorrect. Increasing the standard error makes the confidence interval wider<\/strong>, not narrower. A higher standard error implies more variability and less precision in the estimate.<\/p>\n\n\n\n

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

      If your goal is to narrow a 95% confidence interval<\/strong>, the most effective method is to increase the sample size<\/strong>. This reduces the standard error and makes your estimate of the population parameter more precise.<\/p>\n","protected":false},"excerpt":{"rendered":"

      We could narrow a 95 percent confidence interval by: A. using 99 percent confidence.B. using a larger sample.C. raising the standard error. The correct answer and explanation is : Correct Answer: B. using a larger sample. Explanation: A 95% confidence interval (CI) is a statistical range used to estimate an unknown population parameter (such as […]<\/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-210419","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/210419","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=210419"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/210419\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=210419"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=210419"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=210419"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}