An automobile manufacturer has given its jeep a 56.1 miles\/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep performs under the manufacturer’s MPG rating. After testing 200 jeeps, they found a mean MPG of 56.0. Assume the population standard deviation is known to be 2.1.
Is there sufficient evidence at the 0.02 level to support the testing firm’s claim?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To determine whether there is sufficient evidence to support the claim that the jeep’s actual MPG is lower than the manufacturer’s rating of 56.1 MPG, we can perform a hypothesis test.<\/p>\n\n\n\n From the testing firm\u2019s data:<\/p>\n\n\n\n The significance level ((\\alpha)) is set at 0.02.<\/p>\n\n\n\n We can use the z-test for the mean since the population standard deviation is known. The test statistic (z) can be calculated using the formula: For a one-tailed test at (\\alpha = 0.02), we look up the z-value in the z-table. The critical value for a one-tailed test at the 0.02 level is approximately -2.05.<\/p>\n\n\n\n Now, we compare the calculated z-value to the critical z-value:<\/p>\n\n\n\n Since (-0.673) is greater than (-2.05), we fail to reject the null hypothesis.<\/p>\n\n\n\n There is insufficient evidence at the 0.02 significance level to support the claim that the actual MPG of the jeep is lower than the manufacturer’s rating of 56.1 MPG. The results suggest that while the mean MPG observed was slightly lower than the manufacturer’s claim, it is not statistically significant at the specified level of significance.<\/p>\n","protected":false},"excerpt":{"rendered":" An automobile manufacturer has given its jeep a 56.1 miles\/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep performs under the manufacturer’s MPG rating. After testing 200 jeeps, they found a mean MPG of 56.0. Assume the population standard […]<\/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-146177","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146177","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=146177"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146177\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=146177"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=146177"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=146177"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Formulate the Hypotheses<\/h3>\n\n\n\n
\n
[
H_0: \\mu = 56.1
]<\/li>\n\n\n\n
[
H_1: \\mu < 56.1
]<\/li>\n<\/ul>\n\n\n\nStep 2: Gather Data<\/h3>\n\n\n\n
\n
Step 3: Determine the Significance Level<\/h3>\n\n\n\n
Step 4: Calculate the Test Statistic<\/h3>\n\n\n\n
[
z = \\frac{\\bar{x} – \\mu}{\\sigma\/\\sqrt{n}}
]
Substituting in the values:
[
z = \\frac{56.0 – 56.1}{2.1\/\\sqrt{200}} = \\frac{-0.1}{2.1\/\\sqrt{200}} \\approx \\frac{-0.1}{0.1485} \\approx -0.673
]<\/p>\n\n\n\nStep 5: Determine the Critical Value<\/h3>\n\n\n\n
Step 6: Make a Decision<\/h3>\n\n\n\n
\n
Conclusion<\/h3>\n\n\n\n