{"id":249803,"date":"2025-07-09T21:41:18","date_gmt":"2025-07-09T21:41:18","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=249803"},"modified":"2025-07-09T21:41:21","modified_gmt":"2025-07-09T21:41:21","slug":"expedia-would-like-to-test-the-hypothesis-that-the-average-round-trip-airfare-between-orlando-and-salt-lake-is-the-same-for-a-flight-originating-in-orlando-when-compared-to-a-flight-originating-in-sal","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/09\/expedia-would-like-to-test-the-hypothesis-that-the-average-round-trip-airfare-between-orlando-and-salt-lake-is-the-same-for-a-flight-originating-in-orlando-when-compared-to-a-flight-originating-in-sal\/","title":{"rendered":"Expedia would like to test the hypothesis that the average round trip airfare between Orlando and Salt Lake is the same for a flight originating in Orlando when compared to a flight originating in Salt Lake."},"content":{"rendered":"\n<pre id=\"preorder-ask-header-text\" class=\"wp-block-preformatted\">Expedia would like to test the hypothesis that the average round trip airfare between Orlando and Salt Lake is the same for a flight originating in Orlando when compared to a flight originating in Salt Lake.<\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-355.png\" alt=\"\" class=\"wp-image-249804\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is&nbsp;<strong>(-$25.14, $33.14)<\/strong>.<\/p>\n\n\n\n<p>Here is a step-by-step explanation of how to arrive at this answer:<\/p>\n\n\n\n<p>This problem requires the calculation of a 95% confidence interval for the difference between two independent population means. Since the population standard deviations are unknown, we use a two-sample t-interval. The problem specifies using 18 degrees of freedom, which corresponds to the formula for a pooled t-interval, as the degrees of freedom are calculated by (n\u2081 + n\u2082 &#8211; 2).<\/p>\n\n\n\n<p><strong>1. Identify the Sample Data:<\/strong><br>Let Population 1 be flights from Orlando and Population 2 be flights from Salt Lake.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Orlando (Sample 1):<\/strong>\n<ul class=\"wp-block-list\">\n<li>Sample Mean (x\u0304\u2081): $171<\/li>\n\n\n\n<li>Sample Standard Deviation (s\u2081): $30<\/li>\n\n\n\n<li>Sample Size (n\u2081): 10<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Salt Lake (Sample 2):<\/strong>\n<ul class=\"wp-block-list\">\n<li>Sample Mean (x\u0304\u2082): $167<\/li>\n\n\n\n<li>Sample Standard Deviation (s\u2082): $32<\/li>\n\n\n\n<li>Sample Size (n\u2082): 10<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>2. Calculate the Difference in Sample Means:<\/strong><br>The difference between the sample means is:<br>x\u0304\u2081 &#8211; x\u0304\u2082 = $171 &#8211; $167 = $4<\/p>\n\n\n\n<p><strong>3. Calculate the Pooled Variance (s_p\u00b2):<\/strong><br>The pooled variance combines the variances of both samples:<br>s_p\u00b2 = [ (n\u2081-1)s\u2081\u00b2 + (n\u2082-1)s\u2082\u00b2 ] \/ (n\u2081 + n\u2082 &#8211; 2)<br>s_p\u00b2 = [ (10-1)(30)\u00b2 + (10-1)(32)\u00b2 ] \/ (10 + 10 &#8211; 2)<br>s_p\u00b2 = [ 9(900) + 9(1024) ] \/ 18<br>s_p\u00b2 = [ 8100 + 9216 ] \/ 18<br>s_p\u00b2 = 17316 \/ 18 = 962<\/p>\n\n\n\n<p><strong>4. Calculate the Standard Error (SE):<\/strong><br>The standard error of the difference between the means is:<br>SE = \u221a[ s_p\u00b2 * (1\/n\u2081 + 1\/n\u2082) ]<br>SE = \u221a[ 962 * (1\/10 + 1\/10) ]<br>SE = \u221a[ 962 * (0.2) ]<br>SE = \u221a192.4 \u2248 13.871<\/p>\n\n\n\n<p><em>5. Determine the Critical t-value (t):<\/em>*<br>For a 95% confidence interval with 18 degrees of freedom, the critical t-value (t*) is 2.101.<\/p>\n\n\n\n<p><strong>6. Calculate the Margin of Error (ME):<\/strong><br>The margin of error is the critical t-value multiplied by the standard error:<br>ME = t* * SE<br>ME = 2.101 * 13.871 \u2248 29.143<\/p>\n\n\n\n<p><strong>7. Construct the Confidence Interval:<\/strong><br>The confidence interval is calculated as (Difference in Means) \u00b1 (Margin of Error):<br>Interval = ($4 &#8211; $29.143, $4 +&nbsp;<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>29.143)Interval=(\u221229.143)<em>I<\/em><em>n<\/em><em>t<\/em><em>er<\/em><em>v<\/em><em>a<\/em><em>l<\/em>=(\u2212<\/code><\/pre>\n\n\n\n<p>25.143, $33.143)<\/p>\n\n\n\n<p>Rounding to two decimal places, the 95% confidence interval for the difference in population means is&nbsp;<strong>(-$25.14, $33.14)<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-57.jpeg\" alt=\"\" class=\"wp-image-249805\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Expedia would like to test the hypothesis that the average round trip airfare between Orlando and Salt Lake is the same for a flight originating in Orlando when compared to a flight originating in Salt Lake. The Correct Answer and Explanation is: The correct answer is&nbsp;(-$25.14, $33.14). Here is a step-by-step explanation of how to [&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-249803","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249803","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=249803"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249803\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=249803"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=249803"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=249803"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}