An automobile manufacturer claims that its jeep has a 36.1 miles\/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this jeep since it is believed that the jeep has an incorrect manufacturer’s MPG rating. After testing 150 jeeps, they found a mean MPG of 35.8. Assume the standard deviation is known to be 2.4. A level of significance of 0.02 will be used. Make a decision to reject or fail to reject the null hypothesis. Make a decision.<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To evaluate the manufacturer’s claim about the jeep’s MPG rating, we can use hypothesis testing. The null hypothesis (H\u2080) and the alternative hypothesis (H\u2081) can be formulated as follows:<\/p>\n\n\n\n Given the following information:<\/p>\n\n\n\n We will use the Z-test for this analysis since the population standard deviation is known. The formula for the Z-test statistic is:<\/p>\n\n\n\n [ Plugging in the values:<\/p>\n\n\n\n [ For a two-tailed test at a significance level of 0.02, we need to find the critical Z-values. Since this is a two-tailed test, we split the alpha level (0.02) into two tails, giving us 0.01 in each tail.<\/p>\n\n\n\n Using a Z-table or calculator, the critical Z-values for \u03b1\/2 = 0.01 are approximately \u00b12.576.<\/p>\n\n\n\n Now, we compare the calculated Z-value with the critical Z-values:<\/p>\n\n\n\n Here, the calculated Z-value is -1.53, which falls within the range of -2.576 and 2.576.<\/p>\n\n\n\n Since the calculated Z-value (-1.53) does not exceed the critical values, we fail to reject the null hypothesis<\/strong>. This indicates that there is insufficient evidence at the 0.02 significance level to conclude that the mean MPG of the jeep is different from the manufacturer’s claim of 36.1 MPG. Therefore, the manufacturer’s MPG rating stands, and the independent testing firm’s result does not significantly challenge that claim.<\/p>\n","protected":false},"excerpt":{"rendered":" An automobile manufacturer claims that its jeep has a 36.1 miles\/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this jeep since it is believed that the jeep has an incorrect manufacturer’s MPG rating. After testing 150 jeeps, they found a mean MPG of 35.8. Assume the standard deviation […]<\/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-157753","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/157753","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=157753"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/157753\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=157753"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=157753"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=157753"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
\n
Step 1: Calculate the test statistic<\/h3>\n\n\n\n
Z = \\frac{x\u0304 – \u03bc}{\u03c3 \/ \\sqrt{n}}
]<\/p>\n\n\n\n
Z = \\frac{35.8 – 36.1}{2.4 \/ \\sqrt{150}} = \\frac{-0.3}{0.196} \\approx -1.53
]<\/p>\n\n\n\nStep 2: Determine the critical value<\/h3>\n\n\n\n
Step 3: Make a decision<\/h3>\n\n\n\n
\n
Conclusion<\/h3>\n\n\n\n