{"id":1007,"date":"2021-05-30T22:20:18","date_gmt":"2021-05-31T02:20:18","guid":{"rendered":"https:\/\/openbooks.macewan.ca\/rcommander\/?post_type=part&#038;p=1007"},"modified":"2024-02-08T14:19:05","modified_gmt":"2024-02-08T19:19:05","slug":"chapter-9-inferences-for-two-population-means","status":"publish","type":"part","link":"https:\/\/openbooks.macewan.ca\/introstats\/part\/chapter-9-inferences-for-two-population-means\/","title":{"raw":"Chapter 9: Inferences for Two Population Means","rendered":"Chapter 9: Inferences for Two Population Means"},"content":{"raw":"Chapters 7 and 8 introduced how to obtain a confidence interval and perform a hypothesis test for the population mean <em>[latex]\\mu[\/latex]<\/em> based on a simple random sample from a population with mean [latex]\\mu[\/latex]. This chapter covers how to obtain a confidence interval and conduct a hypothesis test for the difference between population means [latex]\\mu_1[\/latex] \u2013 [latex]\\mu_2[\/latex].\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nAs a result of completing this chapter, you will be able to do the following:\r\n<ul>\r\n \t<li>Explain the sampling distribution of the difference between two sample means [latex]\\bar{X_1} - \\bar{X_2}[\/latex] for two independent samples.<\/li>\r\n \t<li>State the assumptions for inferences about the difference between two population means based on two independent samples.<\/li>\r\n \t<li>Obtain and interpret a [latex](1 \u2013 \\alpha) \\times 100\\%[\/latex] two-mean conference interval for [latex]\\mu_1[\/latex] \u2013 [latex]\\mu_2[\/latex].<\/li>\r\n \t<li>Conduct a two-mean (sample) <i>t-test<\/i>.<\/li>\r\n \t<li>Determine whether two samples are independent or paired.<\/li>\r\n \t<li>Obtain and interpret a paired <em>t-<\/em>confidence interval.<\/li>\r\n \t<li>Conduct a paired <i>t-test<\/i>.<\/li>\r\n \t<li>Explain the relationship between the results of a hypothesis test at significance level [latex]\\alpha[\/latex] and the corresponding [latex](1 \u2013 \\alpha) \\times 100\\%[\/latex] confidence interval.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>","rendered":"<p>Chapters 7 and 8 introduced how to obtain a confidence interval and perform a hypothesis test for the population mean <em>[latex]\\mu[\/latex]<\/em> based on a simple random sample from a population with mean [latex]\\mu[\/latex]. This chapter covers how to obtain a confidence interval and conduct a hypothesis test for the difference between population means [latex]\\mu_1[\/latex] \u2013 [latex]\\mu_2[\/latex].<\/p>\n<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>As a result of completing this chapter, you will be able to do the following:<\/p>\n<ul>\n<li>Explain the sampling distribution of the difference between two sample means [latex]\\bar{X_1} - \\bar{X_2}[\/latex] for two independent samples.<\/li>\n<li>State the assumptions for inferences about the difference between two population means based on two independent samples.<\/li>\n<li>Obtain and interpret a [latex](1 \u2013 \\alpha) \\times 100\\%[\/latex] two-mean conference interval for [latex]\\mu_1[\/latex] \u2013 [latex]\\mu_2[\/latex].<\/li>\n<li>Conduct a two-mean (sample) <i>t-test<\/i>.<\/li>\n<li>Determine whether two samples are independent or paired.<\/li>\n<li>Obtain and interpret a paired <em>t-<\/em>confidence interval.<\/li>\n<li>Conduct a paired <i>t-test<\/i>.<\/li>\n<li>Explain the relationship between the results of a hypothesis test at significance level [latex]\\alpha[\/latex] and the corresponding [latex](1 \u2013 \\alpha) \\times 100\\%[\/latex] confidence interval.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n","protected":false},"parent":0,"menu_order":9,"template":"","meta":{"pb_part_invisible":false,"pb_part_invisible_string":""},"contributor":[],"license":[],"class_list":["post-1007","part","type-part","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/1007","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts"}],"about":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/types\/part"}],"version-history":[{"count":12,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/1007\/revisions"}],"predecessor-version":[{"id":4845,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/pressbooks\/v2\/parts\/1007\/revisions\/4845"}],"wp:attachment":[{"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/media?parent=1007"}],"wp:term":[{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/contributor?post=1007"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/openbooks.macewan.ca\/introstats\/wp-json\/wp\/v2\/license?post=1007"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}