How I lie with statistics

Based upon a convenience sample conducted by Calluna der Partitionoutsmallwoodedvalley (name changed for anonymity) and myself on the breezy afternoon of Tuesday, April 15, 2008, it has been observed that two out of three male road workers in Copper Atoll (also changed) are not registered to vote. A study by Edward Packard reported a total of 5,367,838 registered North Carolina voters in 2006¹ out of a population of 8,857,000².

H_O: There is no statistically significant difference between the proportion of male road workers in Copper Atoll who are registered to vote and the proportion of N.C. citizens at large who are registered to vote.

H_A: There is a statistically significant difference between the proportion of male road workers in Copper Atoll who are registered to vote and the proportion of N.C. citizens at large who are registered to vote.


Rejection criteria: alpha .05, Zsc 1.96

p = 0.6061
q = 0.3939
n = 3

S_p = √((0.6061x0.3939)/3) = 0.2821

Zsc = (0.6666-0.6061)/0.2821 = 0.2145

Since the test statistic of 0.2145 does not meet or exceed the critical value of 1.96, there is insufficient evidence to conclude there is a statistically significant difference between the proportion of male road workers in Copper Atoll who are registered to vote and the proportion of N.C. citizens at large who are registered to vote. Based upon these sample data I fail to reject the null hypothesis.

¹ http://www.cs.duke.edu/~justin/voting/upload/Precinct_size_report.doc
² http://www.newsobserver.com/news/growth/census/story/840401.html


I am aware that the ridiculously small, exclusively male sample of road workers fails to meet two of the three assumptions necessary for a legitimate one sample z-test and that the small sample size was an influential factor in the rejection of H_O. This is all in good fun. Statistically I must admit that there does not appear to be sufficient evidence to support the hypothesis that there is a statistically significant difference between the proportion of male road workers in Copper Atoll who are registered to vote and the proportion of N.C. citizens at large who are registered to vote, but in my heart I fully accept H_A in all its truth and splendor.