{"id":17820,"date":"2016-09-14T18:38:10","date_gmt":"2016-09-14T18:38:10","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=17820"},"modified":"2016-09-14T18:38:10","modified_gmt":"2016-09-14T18:38:10","slug":"statistics-hypothesis-testing-and-p-values-why-the-table-value-is-doubled-when-testing-%ce%bc%e2%89%a0%ce%bc0","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/statistics-hypothesis-testing-and-p-values-why-the-table-value-is-doubled-when-testing-%ce%bc%e2%89%a0%ce%bc0\/","title":{"rendered":"Statistics: hypothesis testing and p-values: why the table value is doubled when testing \u03bc\u2260\u03bc0<\/sub>"},"content":{"rendered":"

The tutor shows a hypothesis testing example with a p-value.<\/h1>\n

In yesterday’s post<\/a> I brought up p-values. Today I’ll give an example:<\/p>\n

A population is believed to have mean \u03bc0<\/sub>=42.5; a sample of 30 is taken with mean x<\/span>=41.6, standard devation s=28.14. Find the p-value that the population mean indeed is 42.5.<\/strong><\/p>\n

Solution:<\/p>\n

With 30 or more in the sample, we can use the z table, even though we’re using the sample standard deviation:<\/p>\n

z=(41.6-42.5)\/(28.14\/300.5<\/sup>)=-0.175<\/p>\n

z=-0.175 leads to a table value of 0.43. However, a p-value measures the likelihood that z could be as far from 0 next time<\/em>. When testing \u03bc≠\u03bc0<\/sub>, it could show up on the other side, with equal probability, since the normal distribution is symmetric:<\/p>\n

<\/p>\n

In this case, the p-value is 2(0.43) = 0.86. The TI-83 Plus agrees. As a p-value, 0.86 is very high: we must continue to believe that the population mean is indeed 42.5.<\/p>\n

I’ll be talking more about statistics in future posts:)<\/p>\n

Source:<\/p>\n

Harnett, Donald L. and James L. Murphy. Statistical Analysis for Business and Economics<\/u>, first Canadian edition. 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":"

The tutor shows a hypothesis testing example with a p-value. In yesterday’s post I brought up p-values. Today I’ll give an example: A population is believed to have mean \u03bc0=42.5; a sample of 30 is taken with mean x=41.6, standard …<\/p>\n

Statistics: hypothesis testing and p-values: why the table value is doubled when testing \u03bc\u2260\u03bc0<\/sub><\/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":[19],"tags":[1885,1881,1887],"class_list":["post-17820","post","type-post","status-publish","format-standard","hentry","category-statistics","tag-hypothesis-testing","tag-p-value","tag-z-approximation-to-t-statistic"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/17820","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=17820"}],"version-history":[{"count":19,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/17820\/revisions"}],"predecessor-version":[{"id":17840,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/17820\/revisions\/17840"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=17820"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=17820"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=17820"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}