{"id":780,"date":"2014-05-28T14:43:24","date_gmt":"2014-05-28T18:43:24","guid":{"rendered":"http:\/\/willistonblogs.com\/math\/?p=780"},"modified":"2014-05-28T14:43:48","modified_gmt":"2014-05-28T18:43:48","slug":"statistics-projects","status":"publish","type":"post","link":"https:\/\/willistonblogs.com\/math\/statistics-projects\/","title":{"rendered":"Statistics Projects"},"content":{"rendered":"<p class=\"p1\">Juniors in the AP Statistics class had the opportunity, this year, to work on a project in the style of a statistical consultant.\u00a0 Students used real data from the 50 States and had their choice of variables to examine.\u00a0 Many of the projects looked at patterns and relationships among various social indicators such as crime, income, education, etc.\u00a0 We looked for trends and associations using a sophisticated statistical programming language called \u201cR\u201d.\u00a0 This was an ambitious task, but the students jumped right in and turned in some of their finest work!\u00a0 Please enjoy the following excerpts from their work.<\/p>\n<p class=\"p1\"><span style=\"text-decoration: underline\"><strong>Ty Lee &#8211; Education trends in the 50 States<\/strong><\/span><\/p>\n<p class=\"p2\"><a href=\"http:\/\/willistonblogs.com\/math\/files\/2014\/05\/image001.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-777\" src=\"http:\/\/willistonblogs.com\/math\/files\/2014\/05\/image001.jpg\" alt=\"image001\" width=\"365\" height=\"370\" srcset=\"https:\/\/willistonblogs.com\/math\/files\/2014\/05\/image001.jpg 365w, https:\/\/willistonblogs.com\/math\/files\/2014\/05\/image001-295x300.jpg 295w\" sizes=\"(max-width: 365px) 100vw, 365px\" \/><\/a><\/p>\n<p class=\"p1\">This histogram visualizes the distribution of the percent of the state population with a bachelor&#8217;s degree or higher. Height of boxes indicate the number of states that fall into the range from the left end to the right end. The state with lowest rate was West Virginia, while the highest was District of Columbia. The shape of this histogram seems to indicate that the underlying population is normal; the graph is uni-modal, not skewed, and looks similar to a bell curve.<\/p>\n<p class=\"p1\"><span style=\"text-decoration: underline\"><strong>Cade Zawacki \u2013 Statistical Analysis Casts Doubt on a Claim about Gun Violence<\/strong><\/span><\/p>\n<p class=\"p1\" style=\"text-align: center\"><em>\u201cIf you look at all the fiascos that have occurred, 99 percent of them have been by Democrats pulling their guns out and shooting people,\u201d Kiehne said. \u201cSo I don\u2019t think you have a problem with the Republicans.\u201d<\/em><\/p>\n<p class=\"p1\"><strong>Chi-Data:<\/strong><br \/>\n<strong>(Does NOT include outliers CO + CT)<\/strong><\/p>\n<p class=\"p1\">(Observed &#8211; Expected) ^2 \/ (Expected)<\/p>\n<p class=\"p1\">Blue: 0.2821752532<br \/>\nRed:\u00a0 0.6195867769 \u00a0 +<br \/>\nSum: 0.9017620301<\/p>\n<p>Chi-Squared cdf(0.9017620301,e99,1) = 0.3423096854<\/p>\n<p class=\"p2\">\u00a0With a Chi-Squared value of about 0.902, we can expect to see results like this about 34% of the time &#8211; assuming that mass shootings happen randomly in any state. Thus, we cannot conclude that there is a relationship between mass shootings and political affiliation.<\/p>\n<p class=\"p2\"><a href=\"http:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.38.55-PM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-781\" src=\"http:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.38.55-PM.png\" alt=\"Screen Shot 2014-05-28 at 2.38.55 PM\" width=\"454\" height=\"307\" srcset=\"https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.38.55-PM.png 454w, https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.38.55-PM-300x202.png 300w, https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.38.55-PM-443x300.png 443w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><\/a><\/p>\n<p class=\"p2\">Depicted above: Chi-Squared cdf(0.9017620301,e99,1) = 0.3423096854<br \/>\n(Domain 0&lt;x&lt;2)<\/p>\n<p class=\"p2\">[These results suggests that it is highly likely that the political inclinations of the State have no effect on the occurrence or frequency of mass shootings.\u00a0 This student pointed out that the data limit our conclusions, to a certain degree since we do not have data for the political preferences of individual shooters.]<\/p>\n<p class=\"p2\"><span style=\"text-decoration: underline\"><strong>Norio Chan and Simon Lu \u2013 No Significant Difference in Assault Rates in Red and Blue States<\/strong><\/span><\/p>\n<p class=\"p1\"><a href=\"http:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.39.51-PM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-782\" src=\"http:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.39.51-PM.png\" alt=\"Screen Shot 2014-05-28 at 2.39.51 PM\" width=\"519\" height=\"453\" srcset=\"https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.39.51-PM.png 519w, https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.39.51-PM-300x261.png 300w, https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.39.51-PM-343x300.png 343w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/a><\/p>\n<p class=\"p1\">The graph and the results of the t-test show that we cannot reject the null hypothesis of \u201cno difference in assault rates\u201d.\u00a0 There is no strong evidence to suggest that assault rates are different in blue states and red states.<\/p>\n<p class=\"p2\"><span style=\"text-decoration: underline\"><strong>Gleb Paschenko \u2013 Murder Rates Decrease when High School Graduation Rates Increase<\/strong><\/span><\/p>\n<p class=\"p2\"><a href=\"http:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.40.44-PM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-783\" src=\"http:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.40.44-PM.png\" alt=\"Screen Shot 2014-05-28 at 2.40.44 PM\" width=\"500\" height=\"485\" srcset=\"https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.40.44-PM.png 500w, https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.40.44-PM-300x291.png 300w, https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.40.44-PM-309x300.png 309w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/a><\/p>\n<p class=\"p1\">Although some outliers are present, the association seems to follow a moderately strong negative linear pattern.\u00a0 In states where high school graduation rate is higher, the murder rate per 100,000 is lower.<\/p>\n<p class=\"p2\"><span style=\"text-decoration: underline\"><strong>James Kim &#8211; Are Harsher Sentences Associated with Crime Reduction?<\/strong><\/span><\/p>\n<p class=\"p1\">Correlation Between Strength of Sentence\/Real Execution Rate and Crime Rate<\/p>\n<p class=\"p2\"><a href=\"http:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.41.30-PM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-784\" src=\"http:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.41.30-PM.png\" alt=\"Screen Shot 2014-05-28 at 2.41.30 PM\" width=\"535\" height=\"357\" srcset=\"https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.41.30-PM.png 535w, https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.41.30-PM-300x200.png 300w, https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.41.30-PM-449x300.png 449w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/a> <a href=\"http:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.41.39-PM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-785\" src=\"http:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.41.39-PM.png\" alt=\"Screen Shot 2014-05-28 at 2.41.39 PM\" width=\"539\" height=\"359\" srcset=\"https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.41.39-PM.png 539w, https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.41.39-PM-300x199.png 300w, https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.41.39-PM-450x300.png 450w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/a><\/p>\n<p class=\"p1\">The very high P-Value suggests that there probably is no relationship between the real execution rate and the murder rate. \u00a0 [We might be inclined to believe that those states with more severe penalties might see a reduction in crime.\u00a0 The data was not able to demonstrate that this was the case.]<\/p>\n<p class=\"p1\"><span style=\"text-decoration: underline\"><strong>Emma Lawrence and Sam Atkins \u2013 High School Graduation Rates in Red States and Blue State<\/strong><\/span><\/p>\n<p class=\"p1\"><a href=\"http:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.42.22-PM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-786\" src=\"http:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.42.22-PM.png\" alt=\"Screen Shot 2014-05-28 at 2.42.22 PM\" width=\"678\" height=\"385\" srcset=\"https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.42.22-PM.png 678w, https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.42.22-PM-300x170.png 300w, https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.42.22-PM-500x283.png 500w\" sizes=\"(max-width: 678px) 100vw, 678px\" \/><\/a><\/p>\n<p class=\"p1\">If we use a significance level of .1 then we can reject the null hypothesis of no difference in high school graduation rates due to the p-value being less than .1.\u00a0 There is some evidence to suggest that high school graduation rates are higher in Blue States.\u00a0 [They are certainly more consistent.]<\/p>\n<p class=\"p1\"><span style=\"text-decoration: underline\"><strong>Summary<\/strong><\/span><\/p>\n<p class=\"p1\">In a world of uncertainty, the mind looks for deterministic explanations.\u00a0 Statistics students have learned to talk about uncertainty, supported by quantitative measures, with confidence.\u00a0 We learned that, too often, our preconceived ideas about a population or claims in the media rest on very little data, indeed.\u00a0 Students, you have been entrusted with a powerful tool \u2013 use it for the good of humankind!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Juniors in the AP Statistics class had the opportunity, this year, to work on a project in the style of a statistical consultant.\u00a0 Students used real data from the 50 States and had their choice of variables to examine.\u00a0 Many of the projects looked at patterns and relationships among various social indicators such as crime, &hellip; <a href=\"https:\/\/willistonblogs.com\/math\/statistics-projects\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Statistics Projects<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":53,"featured_media":782,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"_s2mail":"yes","jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[57],"tags":[149,151,150],"class_list":["post-780","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-stats","tag-histogram","tag-projects","tag-student-work-2"],"jetpack_publicize_connections":[],"aioseo_notices":[],"jetpack_featured_media_url":"https:\/\/willistonblogs.com\/math\/files\/2014\/05\/Screen-Shot-2014-05-28-at-2.39.51-PM.png","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p4GnmO-cA","_links":{"self":[{"href":"https:\/\/willistonblogs.com\/math\/wp-json\/wp\/v2\/posts\/780"}],"collection":[{"href":"https:\/\/willistonblogs.com\/math\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/willistonblogs.com\/math\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/willistonblogs.com\/math\/wp-json\/wp\/v2\/users\/53"}],"replies":[{"embeddable":true,"href":"https:\/\/willistonblogs.com\/math\/wp-json\/wp\/v2\/comments?post=780"}],"version-history":[{"count":2,"href":"https:\/\/willistonblogs.com\/math\/wp-json\/wp\/v2\/posts\/780\/revisions"}],"predecessor-version":[{"id":788,"href":"https:\/\/willistonblogs.com\/math\/wp-json\/wp\/v2\/posts\/780\/revisions\/788"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/willistonblogs.com\/math\/wp-json\/wp\/v2\/media\/782"}],"wp:attachment":[{"href":"https:\/\/willistonblogs.com\/math\/wp-json\/wp\/v2\/media?parent=780"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/willistonblogs.com\/math\/wp-json\/wp\/v2\/categories?post=780"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/willistonblogs.com\/math\/wp-json\/wp\/v2\/tags?post=780"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}