To construct a 90% confidence interval for the population mean using the t-distribution, you need to use the critical value<\/strong> (t*) from the t-distribution table. The critical value depends on two factors: the confidence level<\/strong> (90% in this case) and the degrees of freedom<\/strong> (which is calculated as the sample size minus 1).<\/p>\n\n\n\n Here\u2019s how to approach this:<\/p>\n\n\n\n For a 90% confidence interval, you want the middle 90% of the data to fall between your two bounds. This means that the remaining 10% is split equally on both tails of the t-distribution, with 5% in each tail.<\/p>\n\n\n\n The degrees of freedom for the t-distribution is calculated as:df=n\u22121=8\u22121=7df = n – 1 = 8 – 1 = 7df=n\u22121=8\u22121=7<\/p>\n\n\n\n So, your degrees of freedom is 7.<\/p>\n\n\n\n For a 90% confidence level, with 5% in each tail, the corresponding critical value (t*) for 7 degrees of freedom can be found in the t-distribution table.<\/p>\n\n\n\n For df = 7<\/strong> and a confidence level of 90%, the t* value is approximately 1.89<\/strong>.<\/p>\n\n\n\n You use the positive t-value<\/strong> (1.89) because the t-distribution is symmetric, and this value represents the number of standard errors away from the sample mean for the bounds of your confidence interval.<\/p>\n\n\n\n Thus, the correct answer is t = 1.89<\/strong>.<\/p>\n\n\n\n The critical value represents how far away from the sample mean the bounds of your confidence interval will be. The larger the sample size, the closer the critical value will be to 1, but for small samples (like n = 8), the t-value will be greater than 1 because you need more confidence in the estimate due to the variability in smaller samples. The use of the t-distribution instead of the normal distribution reflects this added uncertainty in the estimate.<\/p>\n\n\n\n You are constructing 90% confidence interval for the population mean using the t distribution: If you have a sample size ofn = 8, what value from the t-distribution chart will vou use in your calculation? t =-1.58 0 t = 1,58 0 t = 1.89 0 t -1.86 The Correct Answer and Explanation is: To […]<\/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-247590","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/247590","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=247590"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/247590\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=247590"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=247590"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=247590"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Identify the confidence level<\/h3>\n\n\n\n
Step 2: Determine the degrees of freedom (df)<\/h3>\n\n\n\n
Step 3: Find the critical value (t*) from the t-distribution table<\/h3>\n\n\n\n
Step 4: Interpretation<\/h3>\n\n\n\n
Explanation<\/h3>\n\n\n\n
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