{"id":47839,"date":"2022-04-02T04:14:00","date_gmt":"2022-04-02T04:14:00","guid":{"rendered":"https:\/\/assignmenttutors.net\/blog\/suppose-you-are-told-that-a-95-confidence-interval-for-the-average\/"},"modified":"2022-04-02T04:14:00","modified_gmt":"2022-04-02T04:14:00","slug":"suppose-you-are-told-that-a-95-confidence-interval-for-the-average","status":"publish","type":"post","link":"https:\/\/assignmenttutors.net\/blog\/suppose-you-are-told-that-a-95-confidence-interval-for-the-average\/","title":{"rendered":"Suppose you are told that a 95% confidence interval for the average"},"content":{"rendered":"<div>\n<p>Questions:<\/p>\n<p>2. Suppose you are told that a 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $3.15 to $3.45. Use the fact that the confidence interval for the mean has the form x \u2013 E to\u00a0 x\u00a0 + E to compute the sample mean and the maximal margin of error E.<\/p>\n<p>4. \u00a0Any state Auto Insurance Company took a random sample of 370 insurance claims paid out during a 1-year period.\u00a0 The average claim paid was $1570. Assume \u00f3 = $250.\u00a0 Find 0.90 and 0.99 confidence intervals for the mean claim payment.<\/p>\n<p>5.\u00a0 Three experiments investigating the relationship between need for cognitive closure and persuasion were reported in \u201cMotivated Resistance and Openness to Persuasion in the Presence or Absence of Prior Information\u201d by A.W. Kruglanski (Journal of Personality and Social Psychology, Vol. 65, No. 5 pp. 861-874).\u00a0 Part of the study involved administering a \u201cneed for closure scale\u201d to a group of students enrolled in an introductory psychology course.\u00a0 The \u201cneed for closure scale\u201d has scores ranging from 101 to 201.\u00a0 For the 73 students in the highest quartile of the distribution, the mean score was x =178.70. Assume a population standard deviation of \u00f3 = 7.81.\u00a0 These students were all classified as high on their need for closure.\u00a0 Find a 95% confidence interval for the population mean score \u00b5 on the \u201cneed for closure scale\u201d for all students with a high need for closure.<\/p>\n<p>6.\u00a0 How large a sample is needed in Problem 5 if we wish to be 99% confident that the sample mean score is within 2 points of the population mean score for students who are high on the need for closure?<\/p>\n<p>7.\u00a0 The Wind Mountain archaeological site is located in southwestern New Mexico.\u00a0 Wind Mountain was home to a culture of prehistoric Native Americans called Anasazi.\u00a0 A random sample of excavations at Wind Mountain gave the following depths (in centimeters) from present-day surface grade to the location of significant archaeological artifacts (Source: Mimbres Mogollon Archaeology, by A. Woosley and A. McIntyre, University of New Mexico Press):<\/p>\n<p>85\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 45\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 120\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 80\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 75\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 55\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 65\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 60<\/p>\n<p>65\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 95\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 90\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 70\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 75\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 65\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 68<\/p>\n<p>a) Use a calculator with mean and sample standard deviation keys to verify thatx\u224874.2 cm and s \u224818.3 cm.<\/p>\n<p>b) Compute a 95% confidence interval for the mean depth \u00b5 at which archaeological artifacts from the Wind Mountain excavation site can be found.<\/p>\n<p>8.\u00a0 Shards of clay vessels were put together to reconstruct rim diameters of the original ceramic vessels found at the Wind Mountain archaeological site (see source in Problem 7).\u00a0 A random sample of ceramic vessels gave the following rim diameters (in centimeters):<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 15.9\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 13.4\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 22.1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 12.7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 13.1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 19.6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 11.7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 13.5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 17.7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 18.1<\/p>\n<p>\u00a0<\/p>\n<p>a)\u00a0\u00a0\u00a0\u00a0\u00a0 Use a calculator with mean and sample standard deviation keys to verify that x \u2248 15.8 cm and s \u2248 3.5 cm.<\/p>\n<p>b)\u00a0\u00a0\u00a0\u00a0\u00a0 Compute an 80% confidence interval for the population mean \u00b5 of rim diameters for such ceramic vessels found at the Wind Mountain archaeological site.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Questions: 2. Suppose you are told that a 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $3.15 to $3.45. Use the fact that the confidence interval for the mean has the form x \u2013 E to\u00a0 x\u00a0 + E to compute the sample mean and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"class_list":["post-47839","post","type-post","status-publish","format-standard","hentry","category-education"],"_links":{"self":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/47839","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/comments?post=47839"}],"version-history":[{"count":0,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/47839\/revisions"}],"wp:attachment":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/media?parent=47839"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/categories?post=47839"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/tags?post=47839"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}