{"id":3281,"date":"2022-09-30T09:05:45","date_gmt":"2022-09-30T03:20:45","guid":{"rendered":"https:\/\/dorjegurung.com\/sciblog\/?p=3281"},"modified":"2022-09-30T09:08:41","modified_gmt":"2022-09-30T03:23:41","slug":"sat-test-cheating-and-statistics","status":"publish","type":"post","link":"https:\/\/www.dorjegurung.com\/sciblog\/sat-test-cheating-and-statistics\/","title":{"rendered":"SAT Test, Cheating, and Statistics"},"content":{"rendered":"\n

This is another one in the problem solving series. And it’s a little involved.<\/p>\n\n\n\n

I have been running SAT (Scholastic Aptitude Test) coaching classes for some time now. And one of the things we do is give them mock tests once a week.<\/p>\n\n\n\n

One time, two of the answer sheets had an unusually high number of answers that matched, including the ones that were wrong.<\/p>\n\n\n\n

Here’s they are.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

Look closely and you’ll notice that the first 31 answers the two students provided are exactly the same, including the wrong ones!<\/p>\n\n\n\n

Assuming the two students did NOT cheat, what is the chance or probability that this could happen randomly? In other words, statistically, what’s the likelihood of that happening?<\/p>\n\n\n\n

Again, like all the other problems of these kinds, it can be solved by modeling. If you know statistics, it can be solved quite readily using statistical formula too.<\/p>\n\n\n\n

However, the similarities in answers sheets of these two students didn’t end or stop there. In the next mock test too, a number of answers were found to be the same, though not as many.<\/p>\n\n\n\n

Here are the answer sheets.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

As you can see from the images above, this time around, 13 of the first 31 answers are the same.<\/p>\n\n\n\n

So, the next question is: what are the chances that both 31 in the first test AND 13 in the test that followed are the same?<\/p>\n\n\n\n

(Incidentally, this is the seventh problem in the series of blog posts about challenging problems. Click\u00a0here<\/a>,\u00a0here<\/a>,\u00a0here<\/a>, here<\/a>, here<\/a>, and here<\/a> for the first six. Click here<\/a> for a description of the reason behind the series and what modeling means in this context.)<\/p>\n","protected":false},"excerpt":{"rendered":"

Seventh one in the series, this blog post is a problem about the chances that two multiple choice answer sheets could have many answer the same, including the wrong ones.<\/p>\n","protected":false},"author":6,"featured_media":3299,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[26],"tags":[77,36,78],"class_list":["post-3281","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-enrichment-activities","tag-analysis","tag-logical-deduction","tag-problem-solving"],"blocksy_meta":[],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/www.dorjegurung.com\/sciblog\/wp-content\/uploads\/2022\/09\/SAT-answer-sheets-featimage.jpg","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p2Y7Kk-QV","_links":{"self":[{"href":"https:\/\/www.dorjegurung.com\/sciblog\/wp-json\/wp\/v2\/posts\/3281","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.dorjegurung.com\/sciblog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.dorjegurung.com\/sciblog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.dorjegurung.com\/sciblog\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/www.dorjegurung.com\/sciblog\/wp-json\/wp\/v2\/comments?post=3281"}],"version-history":[{"count":0,"href":"https:\/\/www.dorjegurung.com\/sciblog\/wp-json\/wp\/v2\/posts\/3281\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.dorjegurung.com\/sciblog\/wp-json\/wp\/v2\/media\/3299"}],"wp:attachment":[{"href":"https:\/\/www.dorjegurung.com\/sciblog\/wp-json\/wp\/v2\/media?parent=3281"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.dorjegurung.com\/sciblog\/wp-json\/wp\/v2\/categories?post=3281"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.dorjegurung.com\/sciblog\/wp-json\/wp\/v2\/tags?post=3281"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}