A “rigged” election? Chance (Spring 2004) presented data from a recent election held to de...

A “rigged” election? Chance (Spring 2004) presented data from a recent election held to determine the board of directors of a local community. There were 27 candidates for the board, and each of 5,553 voters was allowed to choose 6 candidates. The claim was that “a fixed vote with fixed percentages [was] assigned to each and every candidate, making it impossible to participate in an honest election.” Votes were tallied in six time slots: after 600 total votes were in, after 1,200, after 2,444, after 3,444, after 4,444, and, finally, after 5,553 votes. The data on three of the candidates (Smith, Coppin, and Montes) are shown in the accompanying table and saved in the RIGVOTE file. A residential organization believes that “there was nothing random about the count and tallies for each time slot, and specific unnatural or rigged percentages were being assigned to each and every candidate.” Give your opinion. Is the probability of a candidate receiving votes independent of the time slot, and if so, does this imply a rigged election?

Based on Gelman, A. “55,000 residents desperately need your help!” Chance, Vol. 17, No. 2, Spring 2004.

Rejection region

A Large-Sample Test about (p1 - p2) — Comparing Fractions of Smokers for Two Years

Problem In the past decade, intensive antismoking campaigns have been sponsored by both federal and private agencies. Suppose the American Cancer Society randomly sampled 1,500 adults in 2000 and then sampled 1,750 adults in 2010 to determine whether there was evidence that the percentage of smokers had decreased. The results of the two sample surveys where x1 and x2 represent the numbers of smokers in the 2000 and 2010 samples, respectively. Do these data indicate that the fraction of smokers decreased over this 10-year period? Use α = .05.

Results of Smoking Survey

MINITAB contingency table analysis of data

Contingency Table for Marketing Example