Are Mexican Americans less likely to be selected as jurors? Castaneda v. Partida is a case where the Supreme Court review used the phrase "two or three standard deviations" as a criterion for statistical significance. There were 181,535 persons eligible for jury duty, of whom 143,611 were Mexican Americans. Of the 870 people selected for jury duty, 339 were Mexican Americans. We are interested in finding out if there is an association between being a Mexican American and being selected as a juror.
Formulate this problem using a two-way table of counts. Construct the 2 × 2 table using the variables Mexican American or not and juror or not.
Find the X2 statistic and its P-value. Take the square root to obtain the z statistic for comparing two proportions. This is the statistic that the Supreme Court used in its criterion for statistical significance.