{"id":1874,"date":"2022-01-26T10:36:33","date_gmt":"2022-01-26T10:36:33","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=1874"},"modified":"2022-02-08T22:20:59","modified_gmt":"2022-02-08T22:20:59","slug":"11a-b","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/11a-b\/","title":{"raw":"11A\/B","rendered":"11A\/B"},"content":{"raw":"<table>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><strong>Null Hypothesis Forms<\/strong><\/td>\r\n<td><strong>Alternative Hypothesis Possible Forms<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Proportions<\/strong><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Means <\/strong><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div align=\"center\"><img class=\"alignnone wp-image-1875\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26102722\/Picture14-300x268.jpg\" alt=\"A glass of water\" width=\"948\" height=\"847\" \/><\/div>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>Results<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Taste Test A<\/strong><\/td>\r\n<td>30 people participate.\r\n17 prefer bottled water.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>\u00a0Taste Test B<\/strong><\/td>\r\n<td>30 people participate.\r\n21 prefer bottled water.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>Results<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Taste Test C<\/strong><\/td>\r\n<td>50 people participate.\r\n22 prefer bottled water.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>\u00a0Taste Test D<\/strong><\/td>\r\n<td>100 people participate,\r\n44 prefer bottled water.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>Results<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Taste Test B<\/strong><\/td>\r\n<td>30 people participate.\r\n21 prefer bottled water.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>\u00a0Taste Test D<\/strong><\/td>\r\n<td>100 people participate.\r\n44 prefer bottled water.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>Sample size = 30\r\n\r\nStandard error of \u00a0= 0.091<\/td>\r\n<td><img class=\"alignnone wp-image-1879\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26102743\/Picture510-300x134.png\" alt=\"A bar graph with a curve labeled \u201cSample Proportion p\u201d on the x-axis. It is numbered in increments of 0.1 from 0.2 to 0.8. There is a peak at approximately 0.5.\" width=\"851\" height=\"380\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Sample size = 100\r\n\r\nStandard error of \u00a0= 0.050<\/td>\r\n<td>\u00a0<img class=\"alignnone wp-image-1880\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26102748\/Picture64-300x138.png\" alt=\"A bar graph with a curve labeled \u201cSample Proportion o\u201d on the x-axis. It is numbered in increments of 0.1 from 0.2 to 0.8 with a peak at approximately 0.5.\" width=\"926\" height=\"426\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>Study<\/td>\r\n<td>Results<\/td>\r\n<td><\/td>\r\n<td>Test Statistic<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Taste Test B<\/strong><\/td>\r\n<td>30 people participate.\r\n21 prefer bottled water.<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\u00a0<strong>Taste Test D<\/strong><\/td>\r\n<td>100 people participate.\r\n44 prefer bottled water.<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div style=\"text-align: left;\" align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>Skill or Concept: I can . . .<\/td>\r\n<td>Questions to check your understanding<\/td>\r\n<td>Rating\r\nfrom 1 to 5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Calculate and interpret standardized scores.<\/td>\r\n<td>1\u20133<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use a normal distribution to describe the sampling variability of a sample proportion.<\/td>\r\n<td>4\u20136<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Identify sample size as a factor that affects precision in sampling.<\/td>\r\n<td>7<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Empirical Rule to identify unusual values in a normal distribution.<\/td>\r\n<td>8, 9<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<img class=\"alignnone wp-image-1876\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26102727\/Picture214-300x139.png\" alt=\"A bar graph labeled in increments of 0.1. There is a peak at approximately 0.16.\" width=\"1001\" height=\"464\" \/> <img class=\"alignnone wp-image-1878\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26102737\/Picture4-300x200.jpg\" alt=\"A girl throwing plastic bottles in a bin outside.\" width=\"945\" height=\"630\" \/><img class=\"alignnone wp-image-1877\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26102732\/Picture310-300x96.png\" alt=\"A bar graph labeled \u201cSample Proportion p\u201d on the x-axis. It is numbered in increments of 0.1 from 0.3 to 0.8. There is at peak at approximately 0.57.\" width=\"1247\" height=\"399\" \/><img class=\"alignnone wp-image-1881\" style=\"font-size: 1rem; text-align: initial;\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26102753\/Picture72-300x96.png\" alt=\"A curve with a peak centered at approximately 0.5. The x-axis is labeled in increments of 0.05 from 0.35 to 0.65.\" width=\"944\" height=\"302\" \/> <img class=\"alignnone wp-image-1882\" style=\"font-size: 1rem; text-align: initial;\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26102758\/Picture810-300x69.png\" alt=\"A curve with a peak centered at approximately 0 and numbered in increments of 1 from -3 to 3 on the x-axis. The increments are also labeled in increments of sigma, with mu at 0.\" width=\"1026\" height=\"236\" \/>\r\n\r\nGlossary 11A\r\n<dl id=\"fs-id1170572229168\" class=\"definition\">\r\n \t<dt>conditional<\/dt>\r\n \t<dd id=\"fs-id1170572229174\">assuming a certain condition has to be true.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1170572229190\" class=\"definition\">\r\n \t<dt>null hypothesis<\/dt>\r\n \t<dd id=\"fs-id1170572229195\">a baseline assumption about a population parameter of interest; what we assume to be true to begin with.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1170572482608\" class=\"definition\">\r\n \t<dt>alternative hypothesis<\/dt>\r\n \t<dd id=\"fs-id1170572482614\">what we consider to be plausible if the null hypothesis is false.<\/dd>\r\n<\/dl>\r\nGlossary 11B\r\n<dl id=\"fs-id1170572482683\" class=\"definition\">\r\n \t<dt>test statistic<\/dt>\r\n \t<dd id=\"fs-id1170572482689\">a measure of the distance between the sample statistic and the null hypothesis value in terms of the standard error of the statistic.<\/dd>\r\n<\/dl>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<table>\n<tbody>\n<tr>\n<td><\/td>\n<td><strong>Null Hypothesis Forms<\/strong><\/td>\n<td><strong>Alternative Hypothesis Possible Forms<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>Proportions<\/strong><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>Means <\/strong><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: auto;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1875\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26102722\/Picture14-300x268.jpg\" alt=\"A glass of water\" width=\"948\" height=\"847\" \/><\/div>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><\/td>\n<td>Results<\/td>\n<\/tr>\n<tr>\n<td><strong>Taste Test A<\/strong><\/td>\n<td>30 people participate.<br \/>\n17 prefer bottled water.<\/td>\n<\/tr>\n<tr>\n<td><strong>\u00a0Taste Test B<\/strong><\/td>\n<td>30 people participate.<br \/>\n21 prefer bottled water.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><\/td>\n<td>Results<\/td>\n<\/tr>\n<tr>\n<td><strong>Taste Test C<\/strong><\/td>\n<td>50 people participate.<br \/>\n22 prefer bottled water.<\/td>\n<\/tr>\n<tr>\n<td><strong>\u00a0Taste Test D<\/strong><\/td>\n<td>100 people participate,<br \/>\n44 prefer bottled water.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><\/td>\n<td>Results<\/td>\n<\/tr>\n<tr>\n<td><strong>Taste Test B<\/strong><\/td>\n<td>30 people participate.<br \/>\n21 prefer bottled water.<\/td>\n<\/tr>\n<tr>\n<td><strong>\u00a0Taste Test D<\/strong><\/td>\n<td>100 people participate.<br \/>\n44 prefer bottled water.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr>\n<td>Sample size = 30<\/p>\n<p>Standard error of \u00a0= 0.091<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1879\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26102743\/Picture510-300x134.png\" alt=\"A bar graph with a curve labeled \u201cSample Proportion p\u201d on the x-axis. It is numbered in increments of 0.1 from 0.2 to 0.8. There is a peak at approximately 0.5.\" width=\"851\" height=\"380\" \/><\/td>\n<\/tr>\n<tr>\n<td>Sample size = 100<\/p>\n<p>Standard error of \u00a0= 0.050<\/td>\n<td>\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1880\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26102748\/Picture64-300x138.png\" alt=\"A bar graph with a curve labeled \u201cSample Proportion o\u201d on the x-axis. It is numbered in increments of 0.1 from 0.2 to 0.8 with a peak at approximately 0.5.\" width=\"926\" height=\"426\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr>\n<td>Study<\/td>\n<td>Results<\/td>\n<td><\/td>\n<td>Test Statistic<\/td>\n<\/tr>\n<tr>\n<td><strong>Taste Test B<\/strong><\/td>\n<td>30 people participate.<br \/>\n21 prefer bottled water.<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\u00a0<strong>Taste Test D<\/strong><\/td>\n<td>100 people participate.<br \/>\n44 prefer bottled water.<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div style=\"text-align: left; margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td>Skill or Concept: I can . . .<\/td>\n<td>Questions to check your understanding<\/td>\n<td>Rating<br \/>\nfrom 1 to 5<\/td>\n<\/tr>\n<tr>\n<td>Calculate and interpret standardized scores.<\/td>\n<td>1\u20133<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Use a normal distribution to describe the sampling variability of a sample proportion.<\/td>\n<td>4\u20136<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Identify sample size as a factor that affects precision in sampling.<\/td>\n<td>7<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Use the Empirical Rule to identify unusual values in a normal distribution.<\/td>\n<td>8, 9<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1876\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26102727\/Picture214-300x139.png\" alt=\"A bar graph labeled in increments of 0.1. There is a peak at approximately 0.16.\" width=\"1001\" height=\"464\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1878\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26102737\/Picture4-300x200.jpg\" alt=\"A girl throwing plastic bottles in a bin outside.\" width=\"945\" height=\"630\" \/><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1877\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26102732\/Picture310-300x96.png\" alt=\"A bar graph labeled \u201cSample Proportion p\u201d on the x-axis. It is numbered in increments of 0.1 from 0.3 to 0.8. There is at peak at approximately 0.57.\" width=\"1247\" height=\"399\" \/><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1881\" style=\"font-size: 1rem; text-align: initial;\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26102753\/Picture72-300x96.png\" alt=\"A curve with a peak centered at approximately 0.5. The x-axis is labeled in increments of 0.05 from 0.35 to 0.65.\" width=\"944\" height=\"302\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1882\" style=\"font-size: 1rem; text-align: initial;\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26102758\/Picture810-300x69.png\" alt=\"A curve with a peak centered at approximately 0 and numbered in increments of 1 from -3 to 3 on the x-axis. The increments are also labeled in increments of sigma, with mu at 0.\" width=\"1026\" height=\"236\" \/><\/p>\n<p>Glossary 11A<\/p>\n<dl id=\"fs-id1170572229168\" class=\"definition\">\n<dt>conditional<\/dt>\n<dd id=\"fs-id1170572229174\">assuming a certain condition has to be true.<\/dd>\n<\/dl>\n<dl id=\"fs-id1170572229190\" class=\"definition\">\n<dt>null hypothesis<\/dt>\n<dd id=\"fs-id1170572229195\">a baseline assumption about a population parameter of interest; what we assume to be true to begin with.<\/dd>\n<\/dl>\n<dl id=\"fs-id1170572482608\" class=\"definition\">\n<dt>alternative hypothesis<\/dt>\n<dd id=\"fs-id1170572482614\">what we consider to be plausible if the null hypothesis is false.<\/dd>\n<\/dl>\n<p>Glossary 11B<\/p>\n<dl id=\"fs-id1170572482683\" class=\"definition\">\n<dt>test statistic<\/dt>\n<dd id=\"fs-id1170572482689\">a measure of the distance between the sample statistic and the null hypothesis value in terms of the standard error of the statistic.<\/dd>\n<\/dl>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":23592,"menu_order":38,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1874","chapter","type-chapter","status-publish","hentry"],"part":704,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1874","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/23592"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1874\/revisions"}],"predecessor-version":[{"id":2969,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1874\/revisions\/2969"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/704"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/1874\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=1874"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=1874"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=1874"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=1874"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}