{"id":190911,"date":"2025-02-14T03:40:29","date_gmt":"2025-02-14T03:40:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=190911"},"modified":"2025-02-14T03:40:32","modified_gmt":"2025-02-14T03:40:32","slug":"which-z-score-is-used-in-a-a-90-b-98-and-c-99-9-confidence-interval-for-a-population-proportion","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/14\/which-z-score-is-used-in-a-a-90-b-98-and-c-99-9-confidence-interval-for-a-population-proportion\/","title":{"rendered":"Which z-score is used in a (a) 90%, (b) 98%, and (c) 99.9% confidence interval for a population proportion"},"content":{"rendered":"\n

Which z-score is used in a (a) 90%, (b) 98%, and (c) 99.9% confidence interval for a population proportion? a. The Z-score used in a 90% confidence interval for a population proportion is 1 (Round to two decimal places as needed.) b. The Z-score used in a 98% confidence interval for a population proportion is (Round to two decimal places as needed.) c. The Z-score used in a 99.9% confidence interval for a population proportion is (Round to two decimal places as needed.)<\/p>\n\n\n\n

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

The critical z-scores for different confidence intervals are as follows:<\/p>\n\n\n\n

a. 90% confidence interval<\/strong> \u2192 1.645<\/strong>
b. 98% confidence interval<\/strong> \u2192 2.33<\/strong>
c. 99.9% confidence interval<\/strong> \u2192 3.29<\/strong><\/p>\n\n\n\n

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

The z-score (also known as the critical value) represents the number of standard deviations a value is from the mean in a standard normal distribution. In confidence interval estimation, it is used to determine the margin of error around a sample statistic when estimating a population parameter.<\/p>\n\n\n\n

Understanding How Z-Scores Are Found<\/strong><\/h4>\n\n\n\n

To determine the z-score for a confidence interval, we look at the area under the normal curve corresponding to the desired confidence level. This area represents the proportion of values that fall within the given range.<\/p>\n\n\n\n

    \n
  1. 90% Confidence Interval<\/strong><\/li>\n<\/ol>\n\n\n\n
      \n
    • A 90% confidence interval means 90% of the data falls within this range, leaving 5% in each tail<\/strong> (since the normal distribution is symmetrical).<\/li>\n\n\n\n
    • We look up the cumulative probability of 0.9500 (since 90% is in the middle, the remaining 10% is split equally, leaving 5% in the upper tail).<\/li>\n\n\n\n
    • This corresponds to z = 1.645<\/strong>.<\/li>\n<\/ul>\n\n\n\n
        \n
      1. 98% Confidence Interval<\/strong><\/li>\n<\/ol>\n\n\n\n
          \n
        • Here, 98% of the data is within the interval, leaving 1% in each tail<\/strong>.<\/li>\n\n\n\n
        • Looking up the cumulative probability of 0.9900, the z-score is 2.33<\/strong>.<\/li>\n<\/ul>\n\n\n\n
            \n
          1. 99.9% Confidence Interval<\/strong><\/li>\n<\/ol>\n\n\n\n
              \n
            • This confidence level leaves 0.05% in each tail<\/strong>.<\/li>\n\n\n\n
            • The cumulative probability for 99.95% is 3.29<\/strong>.<\/li>\n<\/ul>\n\n\n\n

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

              The higher the confidence level, the wider the confidence interval and the larger the z-score. This means that as we increase confidence, we need to account for more variability, making the interval wider.<\/p>\n","protected":false},"excerpt":{"rendered":"

              Which z-score is used in a (a) 90%, (b) 98%, and (c) 99.9% confidence interval for a population proportion? a. The Z-score used in a 90% confidence interval for a population proportion is 1 (Round to two decimal places as needed.) b. The Z-score used in a 98% confidence interval for a population proportion is […]<\/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-190911","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190911","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=190911"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190911\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=190911"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=190911"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=190911"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}