{"id":26328,"date":"2017-11-28T19:38:33","date_gmt":"2017-11-28T19:38:33","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=26328"},"modified":"2017-11-28T19:38:33","modified_gmt":"2017-11-28T19:38:33","slug":"statistics-how-often-can-something-better-be-expected-to-perform-better","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/statistics-how-often-can-something-better-be-expected-to-perform-better\/","title":{"rendered":"Statistics: how often can something “better” be expected to perform better?"},"content":{"rendered":"

Tutoring statistics, you might imagine everyday situations. The tutor brings up one.<\/h1>\n

Let’s imagine we have two mile runners. Runner 1, called R1, has mean time 4:45, with standard deviation 10s; R2 has mean time 5:00 with standard deviation 12s.<\/p>\n

In any given race, give the probability R1 will beat R2.<\/p>\n

Solution:<\/p>\n

First, we convert the mile times to seconds: R1’s mean is 285s, while R2’s is 300.<\/p>\n

The expected difference between R2 and R1’s time is 300-285=15.<\/p>\n

We can’t add standard deviations, but rather variances: 10^2 + 12^2 = 244. The standard deviation of the difference is then 244^0.5 = 15.6.<\/p>\n

The standardized statistic is z = (x-15)\/15.6. We wonder p(x>0), which means p(z>-0.96). From the z-table, the answer is 0.8315.<\/p>\n

So, R1 should beat R2 about 83% of the time.<\/p>\n

Source:<\/p>\n

Harnett, Donald L. and James L. Murphy. Statistical Analysis for Business and Economics<\/i>. Don Mills: Addison-Wesley, 1993.<\/p>\n

Jack of Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"

Tutoring statistics, you might imagine everyday situations. The tutor brings up one. Let’s imagine we have two mile runners. Runner 1, called R1, has mean time 4:45, with standard deviation 10s; R2 has mean time 5:00 with standard deviation 12s. …<\/p>\n

Statistics: how often can something “better” be expected to perform better?<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2128,19],"tags":[2615,718],"class_list":["post-26328","post","type-post","status-publish","format-standard","hentry","category-probability","category-statistics","tag-how-often-a-faster-runner-will-win","tag-probability"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/26328","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=26328"}],"version-history":[{"count":47,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/26328\/revisions"}],"predecessor-version":[{"id":26375,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/26328\/revisions\/26375"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=26328"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=26328"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=26328"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}