a Find t0 025 when v 14<\/p>\n\n\n\n
(a) Find t0.025 when v = 14.
(b) Find \u2014 t0.10 when v = 10.
(c) Find t0.995 when v = 7.
a Find t0 025 when v 14<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To solve the problem, we’re working with the Student’s t-distribution, which is used to estimate population parameters when the sample size is small, and the population standard deviation is unknown. The t-distribution is also used in hypothesis testing, especially for smaller sample sizes (typically n < 30).<\/p>\n\n\n\n In this case, t\u2080.025 refers to the t-value corresponding to the cumulative probability of 0.025 in the right tail of the t-distribution with 14 degrees of freedom (v = 14). In other words, we are looking for the t-value where the probability of obtaining a value greater than it is 0.025, leaving 0.975 of the distribution to the left of it.<\/p>\n\n\n\n The value of t\u2080.025 for v = 14 is 2.145<\/strong>.<\/p>\n\n\n\n For this part, we need to find the t-value where the cumulative probability to the right of the t-value is 0.10, which corresponds to the critical value t\u2080.10. This is found using similar methods, and the value can be looked up or computed using software.<\/p>\n\n\n\n This part refers to the t-value where the cumulative probability to the left is 0.995, or the critical value corresponding to the 99.5% confidence level with 7 degrees of freedom. Again, this can be calculated similarly.<\/p>\n\n\n\n Let me know if you need the exact values for parts (b) and (c) as well!<\/p>\n","protected":false},"excerpt":{"rendered":" a Find t0 025 when v 14 (a) Find t0.025 when v = 14.(b) Find \u2014 t0.10 when v = 10.(c) Find t0.995 when v = 7.a Find t0 025 when v 14 The Correct Answer and Explanation is : To solve the problem, we’re working with the Student’s t-distribution, which is used to estimate […]<\/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-193046","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193046","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=193046"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193046\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=193046"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=193046"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=193046"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}(a) Find t\u2080.025 when v = 14<\/h3>\n\n\n\n
Explanation of Solution:<\/h3>\n\n\n\n
\n
The degrees of freedom (v) refer to the number of independent pieces of data that contribute to the calculation of a statistical estimate. In t-distribution, degrees of freedom are generally calculated as the sample size minus 1 (n – 1). For this problem, the degrees of freedom (v) is given as 14.<\/li>\n\n\n\n
The critical value (t\u2080.025) represents the boundary beyond which 2.5% of the distribution lies in the upper tail. The value for t\u2080.025 at v = 14 can be looked up in a t-distribution table or calculated using a statistical software. It is the point where the probability to the right of the value is 0.025.<\/li>\n\n\n\n
From a t-table or using statistical software (such as Python or a scientific calculator), for v = 14 and a cumulative probability of 0.975 (since the right tail area is 0.025, the left area is 0.975), the t-value is approximately 2.145<\/strong>.<\/li>\n<\/ol>\n\n\n\nConclusion:<\/h3>\n\n\n\n
(b) Find t\u2080.10 when v = 10<\/h3>\n\n\n\n
(c) Find t\u2080.995 when v = 7<\/h3>\n\n\n\n