# 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).

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).

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).

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

This document is linked from More about Hypothesis Testing.