Did I Get This – Hypothesis Tests for Proportions (Extra Practice)
After reading an article using research done by the Organization for Economic Co-operation and Development (OECD) based in France, a statistics student decided to conduct his own study to see if the figures in the article were accurate. This article stated that 37% of email users said spam has increased in their personal email accounts and 29% said it has increased in their work email accounts.
To test the first figure, let p be the proportion of email users who feel that spam has increased in their personal email. The first set of hypotheses that the student wants to test is then:
Ho: p = 0.37
Ha: p ≠ 0.37
Based upon the data collected by this student, a 95% confidence interval for p was found to be:
(0.25, 0.32).
Based on the collected data, a 95% confidence interval for p was found to be (0.08, 0.14).
http://phhp-faculty-cantrell.sites.medinfo.ufl.edu/files/2013/10/DIG_12025_moreHT.swf
For testing the second figure in the report, let p be the proportion of email users who feel that spam has increased in their work email. The second set of hypotheses that the students wants to test, is then:
Ho: p = 0.29
Ha: p ≠ 0.29
Based upon the data collected by this student, a 95% confidence interval for p was found to be:
(0.273, 0.304).
http://phhp-faculty-cantrell.sites.medinfo.ufl.edu/files/2013/10/DIG_12026_moreHT.swf
According to a study completed in 2006 by Pew Internet, 42% of all Americans had a broadband Internet connection at home. This same statistics student wanted to see if this percentage is different for students at his university.
Ho: p = 0.42
Ha: p ≠ 0.42
Based upon the data the student collected, a 95% confidence interval for p was found to be:
(0.439, 0.457).
http://phhp-faculty-cantrell.sites.medinfo.ufl.edu/files/2013/10/DIG_12027_moreHT.swf
According to the same Pew Internet study, 8% of those with broadband connections are using fixed wireless. let p be the proportion of broadband users who use fixed wireless, and consider the hypotheses:
Ho: p = 0.08
Ha: p ≠ 0.08
http://phhp-faculty-cantrell.sites.medinfo.ufl.edu/files/2013/10/DIG_12028_moreHT.swf
This document is linked from More about Hypothesis Testing.