{"id":282,"date":"2021-07-14T15:59:06","date_gmt":"2021-07-14T15:59:06","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/additional-information-and-full-hypothesis-test-examples\/"},"modified":"2023-12-05T09:35:08","modified_gmt":"2023-12-05T09:35:08","slug":"additional-information-and-full-hypothesis-test-examples","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/additional-information-and-full-hypothesis-test-examples\/","title":{"raw":"Conducting a Full Test","rendered":"Conducting a Full Test"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<section>\r\n<ul id=\"list67\">\r\n \t<li>Conduct a hypothesis test for one mean and interpret the conclusion in context<\/li>\r\n<\/ul>\r\n<\/section><\/div>\r\n<ul id=\"element-162\">\r\n \t<li>In a <strong>hypothesis test<\/strong> problem, you may see words such as \"the level of significance is 1%.\" The \"1%\" is the preconceived or preset <em>\u03b1<\/em>.<\/li>\r\n \t<li>The statistician setting up the hypothesis test selects the value of <em>\u03b1<\/em> to use <strong>before<\/strong> collecting the sample data.<\/li>\r\n \t<li><strong>If no level of significance is given, a common standard to use is <em>\u03b1<\/em> = 0.05.<\/strong><\/li>\r\n \t<li>When you calculate the <em>p<\/em>-value and draw the picture, the <em>p<\/em>-value is the area in the left tail, the right tail, or split evenly between the two tails. For this reason, we call the hypothesis test left, right, or two-tailed.<\/li>\r\n \t<li>The <strong>alternative hypothesis<\/strong>, <em>H<sub>a<\/sub><\/em>, tells you if the test is left, right, or two-tailed. It is the <strong>key<\/strong> to conducting the appropriate test.<\/li>\r\n \t<li><em>H<sub>a<\/sub><\/em> <strong>never<\/strong> has a symbol that contains an equal sign.<\/li>\r\n \t<li><strong>Thinking about the meaning of the<\/strong> <strong><em>p<\/em>-value<\/strong>: A data analyst (and anyone else) should have more confidence that he made the correct decision to reject the null hypothesis with a smaller <em>p<\/em>-value (for example, 0.001 as opposed to 0.04) even if using the 0.05 level for alpha. Similarly, for a large <em>p<\/em>-value such as 0.4, as opposed to a <em>p<\/em>-value of 0.056 (alpha = 0.05 is less than either number), a data analyst should have more confidence that she made the correct decision in not rejecting the null hypothesis. This makes the data analyst use judgment rather than mindlessly applying rules.<\/li>\r\n<\/ul>\r\n<div class=\"textbox examples\">\r\n<h3>Recall: Inequality Symbols<\/h3>\r\nAn inequality is a mathematical statement that compares two expressions using the ideas of greater than or less than.\r\n\r\nHere are some common inequalities seen in Statistics:\r\n<ul>\r\n \t<li>&lt; indicates less than, for example x &lt; 5 indicates x is less than 5<\/li>\r\n \t<li>\u2264 indicates less than or equal to, for example x \u2264 5 indicates x is less than or equal to 5 (5 is included)<\/li>\r\n \t<li>&gt; indicates greater than, for example x &gt; 5 indicates x is greater than 5<\/li>\r\n \t<li>\u2265 indicates greater than or equal to, for example x \u2265 5 indicates x is greater than or equal to 5 (5 is included)<\/li>\r\n<\/ul>\r\n<strong>Note:<\/strong> Where you place the variable in the inequality statement can change the symbol you use.\r\n\r\nFor example:\r\n<ul>\r\n \t<li>x &lt; 5 indicates all possible numbers less than 5.<\/li>\r\n \t<li>5 &lt; x indicates that 5 is less than x, or we could rewrite this with the x on the left: x &gt; 5.<\/li>\r\n<\/ul>\r\n<strong>Note:<\/strong> The inequality is still pointing the same direction relative to x. This statement represents all the real numbers that are greater than 5, which is easier to interpret than 5 is less than x.\r\n\r\n<\/div>\r\n<p id=\"fs-idp42898080\">The following examples illustrate a left-, right-, and two-tailed test.<\/p>\r\n\r\n<div id=\"fs-idp41487520\" class=\"example\" data-type=\"example\">\r\n<div class=\"textbox exercises\">\r\n<h3>Example 1<\/h3>\r\n<p id=\"fs-idp41487648\"><em>H<sub>o<\/sub><\/em>: <em>\u03bc<\/em> = 5, <em>H<sub>a<\/sub><\/em>: <em>\u03bc<\/em> &lt; 5<\/p>\r\n<p id=\"element-343\">Test of a single population mean. <em>H<sub>a<\/sub><\/em> tells you the test is left-tailed. The picture of the <em>p<\/em>-value is as follows:<\/p>\r\n<img class=\"aligncenter wp-image-2050 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/07\/24180600\/9009ac0fc178917a2a44a08ad0a540a2037950d91.jpeg\" alt=\"Normal distribution curve of a single population mean with a value of 5 on the x-axis and the p-value points to the area on the left tail of the curve.\" width=\"487\" height=\"219\" \/>\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp42408528\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\"><header>\r\n<div class=\"textbox key-takeaways\">\r\n<div id=\"fs-idp42408528\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\"><header>\r\n<h3 class=\"title\" data-type=\"title\">TRY IT 1<\/h3>\r\n<\/header>\r\n<div id=\"fs-idp67352928\" class=\"exercise\" data-type=\"exercise\">\r\n<div class=\"problem\" data-type=\"problem\">\r\n<p id=\"eip-idm132446832\"><em>H<sub>0<\/sub><\/em>: <em>\u03bc<\/em> = 10, <em>H<sub>a<\/sub><\/em>: <em>\u03bc<\/em> &lt; 10<\/p>\r\n<p id=\"eip-idp3861728\">Assume the <em>p<\/em>-value is 0.0935. What type of test is this? Draw the picture of the <em>p<\/em>-value.\r\n[reveal-answer q=\"187845\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"187845\"]<\/p>\r\nLeft-tailed test\r\n\r\n<img class=\"alignnone wp-image-1315 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/07\/24000538\/Try-It-1.jpeg\" alt=\"Normal distribution curve of a single population mean with a value of 10 on the x-axis and the p-value points to the area on the left tail of the curve.\" width=\"487\" height=\"208\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/header><\/div>\r\n<div id=\"fs-idp42408528\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\r\n<div id=\"fs-idp67352928\" class=\"exercise\" data-type=\"exercise\">\r\n<div class=\"solution\" data-type=\"solution\">\r\n<div class=\"textbox exercises\">\r\n<h3>Example 2<\/h3>\r\n<div class=\"example\" data-type=\"example\">\r\n\r\n<em>H<sub>0<\/sub><\/em>: <em>p<\/em> \u2264 0.2,\u00a0<em>H<sub>a<\/sub><\/em>: <em>p<\/em> &gt; 0.2\r\n<p id=\"fs-idp117549824\">This is a test of a single population proportion. <em>H<sub>a<\/sub><\/em> tells you the test is <strong>right-tailed<\/strong>. The picture of the <em>p<\/em>-value is as follows:<\/p>\r\n<img class=\"aligncenter wp-image-2052 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/07\/24180649\/1760e78f2b4702649533e8ed193a325ed409c34e.jpeg\" alt=\"Normal distribution curve of a single population proportion with the value of 0.2 on the x-axis. The p-value points to the area on the right tail of the curve.\" width=\"487\" height=\"219\" \/>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idm126098448\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\"><header>\r\n<div class=\"textbox key-takeaways\"><header>\r\n<h3 class=\"title\" data-type=\"title\">TRY IT 2<\/h3>\r\n<\/header>\r\n<div id=\"eip-417\" class=\"exercise\" data-type=\"exercise\">\r\n<div id=\"fs-idp131553552\" class=\"problem\" data-type=\"problem\">\r\n<p id=\"eip-idm89526848\"><em>H<sub>0<\/sub><\/em>: <em>\u03bc<\/em> \u2264 1, <em>H<sub>a<\/sub><\/em>: <em>\u03bc<\/em> &gt; 1<\/p>\r\n<p id=\"eip-idm24425280\">Assume the <em>p<\/em>-value is 0.1243. What type of test is this? Draw the picture of the <em>p<\/em>-value.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/header>\r\n<div id=\"eip-417\" class=\"exercise\" data-type=\"exercise\">\r\n<div id=\"fs-idp131553552\" class=\"problem\" data-type=\"problem\">\r\n<div class=\"textbox exercises\">\r\n<h3>Example 3<\/h3>\r\n<div id=\"fs-idm126098448\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\r\n<div id=\"eip-417\" class=\"exercise\" data-type=\"exercise\">\r\n<div data-type=\"solution\">\r\n\r\n<em>H<sub>0<\/sub><\/em>:\u00a0<em>p<\/em> = 50\u2003\u2003<em>H<sub>a<\/sub><\/em>:\u00a0<em>p<\/em> \u2260 50\r\n\r\nThis is a test of a single population mean. <em>H<sub>a<\/sub><\/em> tells you the test is two-tailed. The picture of the p-value is as follows:\r\n\r\n<img class=\"aligncenter wp-image-2053 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/07\/24180732\/fad6ae155d242729cc8484d4a4367c4a9f2f875a.jpeg\" alt=\"Normal distribution curve of a single population mean with a value of 50 on the x-axis. The p-value formulas, 1\/2(p-value), for a two-tailed test is shown for the areas on the left and right tails of the curve.\" width=\"487\" height=\"219\" \/>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idm63250432\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\"><header>\r\n<div class=\"textbox key-takeaways\"><header>\r\n<h3 class=\"title\" data-type=\"title\">TRY IT 3<\/h3>\r\n<\/header>\r\n<div class=\"exercise\" data-type=\"exercise\">\r\n<div class=\"problem\" data-type=\"problem\">\r\n<p id=\"eip-idp41687312\"><em>H<sub>0<\/sub><\/em>: <em>p<\/em> = 0.5, <em>H<sub>a<\/sub><\/em>: <em>p<\/em> \u2260 0.5<\/p>\r\n<p id=\"eip-idm5668432\">Assume the <em>p<\/em>-value is 0.2564. What type of test is this? Draw the picture of the <em>p<\/em>-value.<\/p>\r\n[reveal-answer q=\"179722\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"179722\"]\r\n<div class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\r\n<div class=\"exercise\" data-type=\"exercise\">\r\n<div class=\"solution ui-solution-visible\" data-type=\"solution\">\r\n<p id=\"eip-303\">Two-tailed test<\/p>\r\n\r\n<figure id=\"fs-idm126590640\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21214711\/CNX_Stats_C09_M09_tryit003annoN.jpg\" alt=\"Normal distribution curve of a single population mean with a value of 0.5 on the x-axis. The p-value formulas, 1\/2(p-value), for a two-tailed test is shown for the areas on the left and right tails of the curve.\" width=\"380\" height=\"208\" data-media-type=\"image\/jpeg\" \/><\/figure>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/header><\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<section>\n<ul id=\"list67\">\n<li>Conduct a hypothesis test for one mean and interpret the conclusion in context<\/li>\n<\/ul>\n<\/section>\n<\/div>\n<ul id=\"element-162\">\n<li>In a <strong>hypothesis test<\/strong> problem, you may see words such as &#8220;the level of significance is 1%.&#8221; The &#8220;1%&#8221; is the preconceived or preset <em>\u03b1<\/em>.<\/li>\n<li>The statistician setting up the hypothesis test selects the value of <em>\u03b1<\/em> to use <strong>before<\/strong> collecting the sample data.<\/li>\n<li><strong>If no level of significance is given, a common standard to use is <em>\u03b1<\/em> = 0.05.<\/strong><\/li>\n<li>When you calculate the <em>p<\/em>-value and draw the picture, the <em>p<\/em>-value is the area in the left tail, the right tail, or split evenly between the two tails. For this reason, we call the hypothesis test left, right, or two-tailed.<\/li>\n<li>The <strong>alternative hypothesis<\/strong>, <em>H<sub>a<\/sub><\/em>, tells you if the test is left, right, or two-tailed. It is the <strong>key<\/strong> to conducting the appropriate test.<\/li>\n<li><em>H<sub>a<\/sub><\/em> <strong>never<\/strong> has a symbol that contains an equal sign.<\/li>\n<li><strong>Thinking about the meaning of the<\/strong> <strong><em>p<\/em>-value<\/strong>: A data analyst (and anyone else) should have more confidence that he made the correct decision to reject the null hypothesis with a smaller <em>p<\/em>-value (for example, 0.001 as opposed to 0.04) even if using the 0.05 level for alpha. Similarly, for a large <em>p<\/em>-value such as 0.4, as opposed to a <em>p<\/em>-value of 0.056 (alpha = 0.05 is less than either number), a data analyst should have more confidence that she made the correct decision in not rejecting the null hypothesis. This makes the data analyst use judgment rather than mindlessly applying rules.<\/li>\n<\/ul>\n<div class=\"textbox examples\">\n<h3>Recall: Inequality Symbols<\/h3>\n<p>An inequality is a mathematical statement that compares two expressions using the ideas of greater than or less than.<\/p>\n<p>Here are some common inequalities seen in Statistics:<\/p>\n<ul>\n<li>&lt; indicates less than, for example x &lt; 5 indicates x is less than 5<\/li>\n<li>\u2264 indicates less than or equal to, for example x \u2264 5 indicates x is less than or equal to 5 (5 is included)<\/li>\n<li>&gt; indicates greater than, for example x &gt; 5 indicates x is greater than 5<\/li>\n<li>\u2265 indicates greater than or equal to, for example x \u2265 5 indicates x is greater than or equal to 5 (5 is included)<\/li>\n<\/ul>\n<p><strong>Note:<\/strong> Where you place the variable in the inequality statement can change the symbol you use.<\/p>\n<p>For example:<\/p>\n<ul>\n<li>x &lt; 5 indicates all possible numbers less than 5.<\/li>\n<li>5 &lt; x indicates that 5 is less than x, or we could rewrite this with the x on the left: x &gt; 5.<\/li>\n<\/ul>\n<p><strong>Note:<\/strong> The inequality is still pointing the same direction relative to x. This statement represents all the real numbers that are greater than 5, which is easier to interpret than 5 is less than x.<\/p>\n<\/div>\n<p id=\"fs-idp42898080\">The following examples illustrate a left-, right-, and two-tailed test.<\/p>\n<div id=\"fs-idp41487520\" class=\"example\" data-type=\"example\">\n<div class=\"textbox exercises\">\n<h3>Example 1<\/h3>\n<p id=\"fs-idp41487648\"><em>H<sub>o<\/sub><\/em>: <em>\u03bc<\/em> = 5, <em>H<sub>a<\/sub><\/em>: <em>\u03bc<\/em> &lt; 5<\/p>\n<p id=\"element-343\">Test of a single population mean. <em>H<sub>a<\/sub><\/em> tells you the test is left-tailed. The picture of the <em>p<\/em>-value is as follows:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2050 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/07\/24180600\/9009ac0fc178917a2a44a08ad0a540a2037950d91.jpeg\" alt=\"Normal distribution curve of a single population mean with a value of 5 on the x-axis and the p-value points to the area on the left tail of the curve.\" width=\"487\" height=\"219\" \/><\/p>\n<\/div>\n<\/div>\n<div id=\"fs-idp42408528\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\n<header>\n<div class=\"textbox key-takeaways\">\n<div id=\"fs-idp42408528\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\"><\/div>\n<\/div>\n<\/header>\n<header>\n<h3 class=\"title\" data-type=\"title\">TRY IT 1<\/h3>\n<\/header>\n<div id=\"fs-idp67352928\" class=\"exercise\" data-type=\"exercise\">\n<div class=\"problem\" data-type=\"problem\">\n<p id=\"eip-idm132446832\"><em>H<sub>0<\/sub><\/em>: <em>\u03bc<\/em> = 10, <em>H<sub>a<\/sub><\/em>: <em>\u03bc<\/em> &lt; 10<\/p>\n<p id=\"eip-idp3861728\">Assume the <em>p<\/em>-value is 0.0935. What type of test is this? Draw the picture of the <em>p<\/em>-value.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q187845\">Show Answer<\/span><\/p>\n<div id=\"q187845\" class=\"hidden-answer\" style=\"display: none\">\n<p>Left-tailed test<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1315 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/07\/24000538\/Try-It-1.jpeg\" alt=\"Normal distribution curve of a single population mean with a value of 10 on the x-axis and the p-value points to the area on the left tail of the curve.\" width=\"487\" height=\"208\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div id=\"fs-idp42408528\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\n<div id=\"fs-idp67352928\" class=\"exercise\" data-type=\"exercise\">\n<div class=\"solution\" data-type=\"solution\">\n<div class=\"textbox exercises\">\n<h3>Example 2<\/h3>\n<div class=\"example\" data-type=\"example\">\n<p><em>H<sub>0<\/sub><\/em>: <em>p<\/em> \u2264 0.2,\u00a0<em>H<sub>a<\/sub><\/em>: <em>p<\/em> &gt; 0.2<\/p>\n<p id=\"fs-idp117549824\">This is a test of a single population proportion. <em>H<sub>a<\/sub><\/em> tells you the test is <strong>right-tailed<\/strong>. The picture of the <em>p<\/em>-value is as follows:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2052 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/07\/24180649\/1760e78f2b4702649533e8ed193a325ed409c34e.jpeg\" alt=\"Normal distribution curve of a single population proportion with the value of 0.2 on the x-axis. The p-value points to the area on the right tail of the curve.\" width=\"487\" height=\"219\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-idm126098448\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\n<header>\n<div class=\"textbox key-takeaways\"><\/div>\n<\/header>\n<header>\n<h3 class=\"title\" data-type=\"title\">TRY IT 2<\/h3>\n<\/header>\n<div id=\"eip-417\" class=\"exercise\" data-type=\"exercise\">\n<div id=\"fs-idp131553552\" class=\"problem\" data-type=\"problem\">\n<p id=\"eip-idm89526848\"><em>H<sub>0<\/sub><\/em>: <em>\u03bc<\/em> \u2264 1, <em>H<sub>a<\/sub><\/em>: <em>\u03bc<\/em> &gt; 1<\/p>\n<p id=\"eip-idm24425280\">Assume the <em>p<\/em>-value is 0.1243. What type of test is this? Draw the picture of the <em>p<\/em>-value.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"eip-417\" class=\"exercise\" data-type=\"exercise\">\n<div id=\"fs-idp131553552\" class=\"problem\" data-type=\"problem\">\n<div class=\"textbox exercises\">\n<h3>Example 3<\/h3>\n<div id=\"fs-idm126098448\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\n<div id=\"eip-417\" class=\"exercise\" data-type=\"exercise\">\n<div data-type=\"solution\">\n<p><em>H<sub>0<\/sub><\/em>:\u00a0<em>p<\/em> = 50\u2003\u2003<em>H<sub>a<\/sub><\/em>:\u00a0<em>p<\/em> \u2260 50<\/p>\n<p>This is a test of a single population mean. <em>H<sub>a<\/sub><\/em> tells you the test is two-tailed. The picture of the p-value is as follows:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2053 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/07\/24180732\/fad6ae155d242729cc8484d4a4367c4a9f2f875a.jpeg\" alt=\"Normal distribution curve of a single population mean with a value of 50 on the x-axis. The p-value formulas, 1\/2(p-value), for a two-tailed test is shown for the areas on the left and right tails of the curve.\" width=\"487\" height=\"219\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-idm63250432\" class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\n<header>\n<div class=\"textbox key-takeaways\"><\/div>\n<\/header>\n<header>\n<h3 class=\"title\" data-type=\"title\">TRY IT 3<\/h3>\n<\/header>\n<div class=\"exercise\" data-type=\"exercise\">\n<div class=\"problem\" data-type=\"problem\">\n<p id=\"eip-idp41687312\"><em>H<sub>0<\/sub><\/em>: <em>p<\/em> = 0.5, <em>H<sub>a<\/sub><\/em>: <em>p<\/em> \u2260 0.5<\/p>\n<p id=\"eip-idm5668432\">Assume the <em>p<\/em>-value is 0.2564. What type of test is this? Draw the picture of the <em>p<\/em>-value.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q179722\">Show Answer<\/span><\/p>\n<div id=\"q179722\" class=\"hidden-answer\" style=\"display: none\">\n<div class=\"note statistics try ui-has-child-title\" data-type=\"note\" data-has-label=\"true\" data-label=\"\">\n<div class=\"exercise\" data-type=\"exercise\">\n<div class=\"solution ui-solution-visible\" data-type=\"solution\">\n<p id=\"eip-303\">Two-tailed test<\/p>\n<figure id=\"fs-idm126590640\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21214711\/CNX_Stats_C09_M09_tryit003annoN.jpg\" alt=\"Normal distribution curve of a single population mean with a value of 0.5 on the x-axis. The p-value formulas, 1\/2(p-value), for a two-tailed test is shown for the areas on the left and right tails of the curve.\" width=\"380\" height=\"208\" data-media-type=\"image\/jpeg\" \/><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-282\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Introductory Statistics. <strong>Authored by<\/strong>: Barbara Illowsky, Susan Dean. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\">https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction<\/li><li>College Algebra. <strong>Authored by<\/strong>: Jay Abramson, et al.. <strong>Provided by<\/strong>: Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/read-describe-solutions-to-inequalities-2\/\">https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/read-describe-solutions-to-inequalities-2\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Unit 10: Solving Equations and Inequalities, from Developmental Math: An Open Program. <strong>Provided by<\/strong>: Monterey Institute of Technology and Education. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/dm-opentext\">http:\/\/nrocnetwork.org\/dm-opentext<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169134,"menu_order":20,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Introductory Statistics\",\"author\":\"Barbara Illowsky, Susan Dean\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\"},{\"type\":\"cc\",\"description\":\"College Algebra\",\"author\":\"Jay Abramson, et al.\",\"organization\":\"Lumen Learning\",\"url\":\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/read-describe-solutions-to-inequalities-2\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen 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