{"id":2670,"date":"2022-04-04T22:23:58","date_gmt":"2022-04-04T22:23:58","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/?post_type=chapter&#038;p=2670"},"modified":"2022-04-04T22:23:58","modified_gmt":"2022-04-04T22:23:58","slug":"module-11-assignment-using-technology-with-data-to-run-a-hypothesis-test","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/chapter\/module-11-assignment-using-technology-with-data-to-run-a-hypothesis-test\/","title":{"raw":"Module 11 Assignment: Using Technology with Data to Run a Hypothesis Test","rendered":"Module 11 Assignment: Using Technology with Data to Run a Hypothesis Test"},"content":{"raw":"The purpose of this activity is to give you guided practice in carrying out the two-sample t-test, and to show you how to use software to aid in the process.\r\n<h2>Background<\/h2>\r\nDo undergraduates sleep less than graduate students? A student conducted a study of sleep habits at a large state university. His hypothesis is that undergraduates will party more and sleep less than graduate students. He surveyed random samples of 75 undergraduate students and 50 graduate students. Subjects reported the hours they sleep in a typical night.\r\n\r\nFor this hypothesis test, he defined the population means as follows:\r\n<ul>\r\n \t<li>\u03bc<sub>1<\/sub>\u00a0is the mean number of hours undergraduate students sleep in a typical night.<\/li>\r\n \t<li>\u03bc<sub>2<\/sub>\u00a0is the mean number of hours graduate students sleep in a typical night.<\/li>\r\n<\/ul>\r\n<h2>Question 1:<\/h2>\r\nState the null and alternative hypotheses that are being tested here.\r\n<h2>Question 2:<\/h2>\r\nExplain why we can safely use the two-sample T-test in this case.\r\n\r\n<strong>Comment:<\/strong>\u00a0Before we move on to carry out the test, it is important to realize that in the two-sample problem, the data can be provided in three possible ways:\r\n\r\n(i) Sample data in one column, and another column that indicates which sample the observation belongs to. Recall that this is the way the data were given in our leading example (looks vs. personality score and gender):\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th>Score (Y)<\/th>\r\n<th>Gender (X)<\/th>\r\n<\/tr>\r\n<tr>\r\n<td>15<\/td>\r\n<td>Male<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>13<\/td>\r\n<td>Female<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>10<\/td>\r\n<td>Female<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>12<\/td>\r\n<td>Male<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>14<\/td>\r\n<td>Female<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>14<\/td>\r\n<td>Male<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>6<\/td>\r\n<td>Male<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>17<\/td>\r\n<td>Male<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\u2026<\/td>\r\n<td>\u2026<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNote that essentially, one column contains the explanatory variable, and one contains the response.\r\n\r\n(ii) Sample data in different columns\u2014data from each of the two samples appear in a column dedicated to that category. As you\u2019ll see, this is the way the data are provided in this example:\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th>Undergraduate<\/th>\r\n<th>Graduate<\/th>\r\n<\/tr>\r\n<tr>\r\n<td>6<\/td>\r\n<td>8<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5<\/td>\r\n<td>5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>6<\/td>\r\n<td>6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\u2026<\/td>\r\n<td>\u2026<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n(iii) Summarized data\u2014we are not given the actual data, but just the data summaries: sample sizes, sample means and sample standard deviations of both samples. Recall that in our second example, the data were given in this format.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th><\/th>\r\n<th>n<\/th>\r\n<th>y-bar<\/th>\r\n<th>S<\/th>\r\n<\/tr>\r\n<tr>\r\n<th>20-29 yrs old<\/th>\r\n<td>712<\/td>\r\n<td>83.4<\/td>\r\n<td>18.7<\/td>\r\n<\/tr>\r\n<tr>\r\n<th>75+ yrs old<\/th>\r\n<td>1001<\/td>\r\n<td>78.5<\/td>\r\n<td>19.0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Instructions<\/h2>\r\nClick on the link corresponding to your statistical package to see instructions for completing the activity, and then answer the questions below.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/_u5_m2_lbd2\/_u5_m2_lbd2_r0.html\" target=\"_blank\" rel=\"noopener\">R\u00a0<\/a>|\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/_u5_m2_lbd2\/_u5_m2_lbd2_statcrunch0.html\" target=\"_blank\" rel=\"noopener\">StatCrunch\u00a0<\/a>|\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/_u5_m2_lbd2\/_u5_m2_lbd2_minitab0.html\" target=\"_blank\" rel=\"noopener\">Minitab\u00a0<\/a>|\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/_u5_m2_lbd2\/_u5_m2_lbd2_excel0.html\" target=\"_blank\" rel=\"noopener\">Excel\u00a0<\/a>|\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/_u5_m2_lbd2\/_u5_m2_lbd2_ti0.html\" target=\"_blank\" rel=\"noopener\">TI Calculator<\/a>\r\n<h2>Question 3:<\/h2>\r\nCarry out the test and report the test statistic and P-value.\r\n<h2>Question 4:<\/h2>\r\nDraw your conclusions in context.","rendered":"<p>The purpose of this activity is to give you guided practice in carrying out the two-sample t-test, and to show you how to use software to aid in the process.<\/p>\n<h2>Background<\/h2>\n<p>Do undergraduates sleep less than graduate students? A student conducted a study of sleep habits at a large state university. His hypothesis is that undergraduates will party more and sleep less than graduate students. He surveyed random samples of 75 undergraduate students and 50 graduate students. Subjects reported the hours they sleep in a typical night.<\/p>\n<p>For this hypothesis test, he defined the population means as follows:<\/p>\n<ul>\n<li>\u03bc<sub>1<\/sub>\u00a0is the mean number of hours undergraduate students sleep in a typical night.<\/li>\n<li>\u03bc<sub>2<\/sub>\u00a0is the mean number of hours graduate students sleep in a typical night.<\/li>\n<\/ul>\n<h2>Question 1:<\/h2>\n<p>State the null and alternative hypotheses that are being tested here.<\/p>\n<h2>Question 2:<\/h2>\n<p>Explain why we can safely use the two-sample T-test in this case.<\/p>\n<p><strong>Comment:<\/strong>\u00a0Before we move on to carry out the test, it is important to realize that in the two-sample problem, the data can be provided in three possible ways:<\/p>\n<p>(i) Sample data in one column, and another column that indicates which sample the observation belongs to. Recall that this is the way the data were given in our leading example (looks vs. personality score and gender):<\/p>\n<table>\n<tbody>\n<tr>\n<th>Score (Y)<\/th>\n<th>Gender (X)<\/th>\n<\/tr>\n<tr>\n<td>15<\/td>\n<td>Male<\/td>\n<\/tr>\n<tr>\n<td>13<\/td>\n<td>Female<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>Female<\/td>\n<\/tr>\n<tr>\n<td>12<\/td>\n<td>Male<\/td>\n<\/tr>\n<tr>\n<td>14<\/td>\n<td>Female<\/td>\n<\/tr>\n<tr>\n<td>14<\/td>\n<td>Male<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>Male<\/td>\n<\/tr>\n<tr>\n<td>17<\/td>\n<td>Male<\/td>\n<\/tr>\n<tr>\n<td>\u2026<\/td>\n<td>\u2026<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Note that essentially, one column contains the explanatory variable, and one contains the response.<\/p>\n<p>(ii) Sample data in different columns\u2014data from each of the two samples appear in a column dedicated to that category. As you\u2019ll see, this is the way the data are provided in this example:<\/p>\n<table>\n<tbody>\n<tr>\n<th>Undergraduate<\/th>\n<th>Graduate<\/th>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>8<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>\u2026<\/td>\n<td>\u2026<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>(iii) Summarized data\u2014we are not given the actual data, but just the data summaries: sample sizes, sample means and sample standard deviations of both samples. Recall that in our second example, the data were given in this format.<\/p>\n<table>\n<tbody>\n<tr>\n<th><\/th>\n<th>n<\/th>\n<th>y-bar<\/th>\n<th>S<\/th>\n<\/tr>\n<tr>\n<th>20-29 yrs old<\/th>\n<td>712<\/td>\n<td>83.4<\/td>\n<td>18.7<\/td>\n<\/tr>\n<tr>\n<th>75+ yrs old<\/th>\n<td>1001<\/td>\n<td>78.5<\/td>\n<td>19.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Instructions<\/h2>\n<p>Click on the link corresponding to your statistical package to see instructions for completing the activity, and then answer the questions below.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/_u5_m2_lbd2\/_u5_m2_lbd2_r0.html\" target=\"_blank\" rel=\"noopener\">R\u00a0<\/a>|\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/_u5_m2_lbd2\/_u5_m2_lbd2_statcrunch0.html\" target=\"_blank\" rel=\"noopener\">StatCrunch\u00a0<\/a>|\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/_u5_m2_lbd2\/_u5_m2_lbd2_minitab0.html\" target=\"_blank\" rel=\"noopener\">Minitab\u00a0<\/a>|\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/_u5_m2_lbd2\/_u5_m2_lbd2_excel0.html\" target=\"_blank\" rel=\"noopener\">Excel\u00a0<\/a>|\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/_u5_m2_lbd2\/_u5_m2_lbd2_ti0.html\" target=\"_blank\" rel=\"noopener\">TI Calculator<\/a><\/p>\n<h2>Question 3:<\/h2>\n<p>Carry out the test and report the test statistic and P-value.<\/p>\n<h2>Question 4:<\/h2>\n<p>Draw your conclusions in context.<\/p>\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-2670\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Concepts in Statistics. <strong>Provided by<\/strong>: Open Learning Initiative. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/oli.cmu.edu\/\">http:\/\/oli.cmu.edu\/<\/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":428269,"menu_order":19,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Concepts in Statistics\",\"author\":\"\",\"organization\":\"Open Learning Initiative\",\"url\":\"http:\/\/oli.cmu.edu\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2670","chapter","type-chapter","status-web-only","hentry"],"part":2599,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/2670","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/users\/428269"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/2670\/revisions"}],"predecessor-version":[{"id":2671,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/2670\/revisions\/2671"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/parts\/2599"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/2670\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/media?parent=2670"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapter-type?post=2670"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/contributor?post=2670"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/license?post=2670"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}